path stringlengths 11 71 | content stringlengths 75 124k |
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Tactic.lean | import Mathlib.Tactic.Abel
import Mathlib.Tactic.AdaptationNote
import Mathlib.Tactic.ApplyAt
import Mathlib.Tactic.ApplyCongr
import Mathlib.Tactic.ApplyFun
import Mathlib.Tactic.ApplyWith
import Mathlib.Tactic.ArithMult
import Mathlib.Tactic.ArithMult.Init
import Mathlib.Tactic.Attr.Core
import Mathlib.Tactic.Attr.Re... |
Algebra\AddTorsor.lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers, Yury Kudryashov
-/
import Mathlib.Data.Set.Pointwise.SMul
/-!
# Torsors of additive group actions
This file defines torsors of additive group actions.
## Notations
The ... |
Algebra\AlgebraicCard.lean | /-
Copyright (c) 2022 Violeta Hernández Palacios. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Violeta Hernández Palacios
-/
import Mathlib.Algebra.Polynomial.Cardinal
import Mathlib.RingTheory.Algebraic
/-!
### Cardinality of algebraic numbers
In this file, we pro... |
Algebra\Bounds.lean | /-
Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import Mathlib.Algebra.Order.Group.OrderIso
import Mathlib.Data.Set.Pointwise.Basic
import Mathlib.Order.Bounds.OrderIso
import Mathlib.Order.ConditionallyCom... |
Algebra\CubicDiscriminant.lean | /-
Copyright (c) 2022 David Kurniadi Angdinata. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Kurniadi Angdinata
-/
import Mathlib.Algebra.Polynomial.Splits
/-!
# Cubics and discriminants
This file defines cubic polynomials over a semiring and their discrimina... |
Algebra\DirectLimit.lean | /-
Copyright (c) 2019 Kenny Lau, Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Chris Hughes, Jujian Zhang
-/
import Mathlib.Data.Finset.Order
import Mathlib.Algebra.DirectSum.Module
import Mathlib.RingTheory.FreeCommRing
import Mathlib.RingThe... |
Algebra\DualNumber.lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.TrivSqZeroExt
/-!
# Dual numbers
The dual numbers over `R` are of the form `a + bε`, where `a` and `b` are typically elements of a
commutative ring... |
Algebra\DualQuaternion.lean | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.DualNumber
import Mathlib.Algebra.Quaternion
/-!
# Dual quaternions
Similar to the way that rotations in 3D space can be represented by quaternions... |
Algebra\Exact.lean | /-
Copyright (c) 2023 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
import Mathlib.Algebra.Module.Submodule.Range
import Mathlib.LinearAlgebra.Prod
import Mathlib.LinearAlgebra.Quotient
/-! # Exactness of a pair
* For... |
Algebra\Expr.lean | /-
Copyright (c) 2022 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.Group.ZeroOne
import Qq
/-! # Helpers to invoke functions involving algebra at tactic time
This file provides instances on `x y : Q($α)` such that ... |
Algebra\Free.lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import Mathlib.Algebra.Group.Equiv.Basic
import Mathlib.Control.Applicative
import Mathlib.Control.Traversable.Basic
import Mathlib.Data.List.Basic
import Mathlib.Logic.Equiv.D... |
Algebra\FreeAlgebra.lean | /-
Copyright (c) 2020 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Adam Topaz, Eric Wieser
-/
import Mathlib.Algebra.Algebra.Subalgebra.Basic
import Mathlib.Algebra.Algebra.Tower
import Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors
import M... |
Algebra\FreeNonUnitalNonAssocAlgebra.lean | /-
Copyright (c) 2021 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.Algebra.Free
import Mathlib.Algebra.MonoidAlgebra.Basic
/-!
# Free algebras
Given a semiring `R` and a type `X`, we construct the free non-unital, non-asso... |
Algebra\GeomSum.lean | /-
Copyright (c) 2019 Neil Strickland. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Neil Strickland
-/
import Mathlib.Algebra.BigOperators.Intervals
import Mathlib.Algebra.BigOperators.Ring
import Mathlib.Algebra.Order.BigOperators.Ring.Finset
import Mathlib.Algebra.... |
Algebra\GradedMonoid.lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.BigOperators.Group.List
import Mathlib.Algebra.Group.InjSurj
import Mathlib.Data.List.FinRange
import Mathlib.Algebra.Group.Action.Defs
import Mathli... |
Algebra\GradedMulAction.lean | /-
Copyright (c) 2022 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang, Eric Wieser
-/
import Mathlib.Algebra.GradedMonoid
/-!
# Additively-graded multiplicative action structures
This module provides a set of heterogeneous typeclasses for de... |
Algebra\HierarchyDesign.lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Eric Wieser
-/
import Batteries.Util.LibraryNote
/-!
# Documentation of the algebraic hierarchy
A library note giving advice on modifying the algebraic hierarchy.
(It... |
Algebra\IsPrimePow.lean | /-
Copyright (c) 2022 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import Mathlib.Algebra.Associated.Basic
import Mathlib.NumberTheory.Divisors
/-!
# Prime powers
This file deals with prime powers: numbers which are positive integer po... |
Algebra\LinearRecurrence.lean | /-
Copyright (c) 2020 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-/
import Mathlib.Algebra.Polynomial.Eval
import Mathlib.LinearAlgebra.Dimension.Constructions
/-!
# Linear recurrence
Informally, a "linear recurrence" is an asse... |
Algebra\ModEq.lean | /-
Copyright (c) 2023 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Data.Int.ModEq
import Mathlib.GroupTheory.QuotientGroup
/-!
# Equality modulo an element
This file defines equality modulo an element in a commutative gr... |
Algebra\NeZero.lean | /-
Copyright (c) 2021 Eric Rodriguez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Rodriguez
-/
import Mathlib.Logic.Basic
import Mathlib.Algebra.Group.ZeroOne
import Mathlib.Order.Defs
/-!
# `NeZero` typeclass
We create a typeclass `NeZero n` which carries ar... |
Algebra\Opposites.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import Mathlib.Algebra.Group.Defs
import Mathlib.Logic.Equiv.Defs
import Mathlib.Logic.Nontrivial.Basic
import Mathlib.Logic.IsEmpty
/-!
# Multiplicative opposite and algebrai... |
Algebra\PEmptyInstances.lean | /-
Copyright (c) 2021 Julian Kuelshammer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Kuelshammer
-/
import Mathlib.Algebra.Group.Defs
import Mathlib.Tactic.ToAdditive
/-!
# Instances on pempty
This file collects facts about algebraic structures on the (uni... |
Algebra\Periodic.lean | /-
Copyright (c) 2021 Benjamin Davidson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Benjamin Davidson
-/
import Mathlib.Algebra.Field.Opposite
import Mathlib.Algebra.Group.Subgroup.ZPowers
import Mathlib.Algebra.Group.Submonoid.Membership
import Mathlib.Algebra.Rin... |
Algebra\QuadraticDiscriminant.lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou
-/
import Mathlib.Order.Filter.AtTopBot
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.LinearCombination
import Mathlib.Tactic.Linarith.Frontend
/-!
# Quadratic di... |
Algebra\Quandle.lean | /-
Copyright (c) 2020 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
import Mathlib.Algebra.Group.Equiv.Basic
import Mathlib.Algebra.Group.Aut
import Mathlib.Data.ZMod.Defs
import Mathlib.Tactic.Ring
/-!
# Racks and Quandles
This file defin... |
Algebra\Quaternion.lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Algebra.Algebra.Equiv
import Mathlib.LinearAlgebra.Dimension.StrongRankCondition
import Mathlib.LinearAlgebra.FreeModule.Basic
import Mathlib.LinearA... |
Algebra\QuaternionBasis.lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.Quaternion
import Mathlib.Tactic.Ring
/-!
# Basis on a quaternion-like algebra
## Main definitions
* `QuaternionAlgebra.Basis A c₁ c₂`: a basis fo... |
Algebra\Quotient.lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import Mathlib.Tactic.Common
/-!
# Algebraic quotients
This file defines notation for algebraic quotients, e.g. quotient groups `G ⧸ H`,
quotient modules `M ⧸ N` and idea... |
Algebra\RingQuot.lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.Algebra.Algebra.Hom
import Mathlib.RingTheory.Ideal.Quotient
/-!
# Quotients of non-commutative rings
Unfortunately, ideals have only been developed ... |
Algebra\SMulWithZero.lean | /-
Copyright (c) 2021 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
import Mathlib.Algebra.Group.Action.Opposite
import Mathlib.Algebra.Group.Action.Prod
import Mathlib.Algebra.GroupWithZero.Action.Defs
import Mathlib.Algebra.GroupWithZ... |
Algebra\Symmetrized.lean | /-
Copyright (c) 2021 Christopher Hoskin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Hoskin
-/
import Mathlib.Algebra.Jordan.Basic
import Mathlib.Algebra.Module.Defs
/-!
# Symmetrized algebra
A commutative multiplication on a real or complex space can... |
Algebra\TrivSqZeroExt.lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Eric Wieser
-/
import Mathlib.Algebra.Algebra.Defs
import Mathlib.GroupTheory.GroupAction.BigOperators
import Mathlib.LinearAlgebra.Prod
/-!
# Trivial Square-Zero Extension
Giv... |
Algebra\AddConstMap\Basic.lean | /-
Copyright (c) 2024 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Algebra.Group.Action.Pi
import Mathlib.Algebra.GroupPower.IterateHom
import Mathlib.Algebra.Module.Defs
import Mathlib.Algebra.Order.Archimedean.Basi... |
Algebra\AddConstMap\Equiv.lean | /-
Copyright (c) 2024 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Algebra.AddConstMap.Basic
import Mathlib.GroupTheory.Perm.Basic
/-!
# Equivalences conjugating `(· + a)` to `(· + b)`
In this file we define `AddCon... |
Algebra\Algebra\Basic.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Yury Kudryashov
-/
import Mathlib.Algebra.Algebra.Defs
import Mathlib.Algebra.CharZero.Lemmas
import Mathlib.Algebra.Module.Equiv.Basic
import Mathlib.Algebra.Module.Submodule.Ke... |
Algebra\Algebra\Bilinear.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Yury Kudryashov
-/
import Mathlib.Algebra.Algebra.Defs
import Mathlib.Algebra.Algebra.NonUnitalHom
import Mathlib.Algebra.GroupPower.IterateHom
import Mathlib.LinearAlgebra.Tenso... |
Algebra\Algebra\Defs.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Yury Kudryashov
-/
import Mathlib.Algebra.BigOperators.Group.Finset
import Mathlib.Algebra.Module.LinearMap.Defs
/-!
# Algebras over commutative semirings
In this file we defin... |
Algebra\Algebra\Equiv.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Yury Kudryashov
-/
import Mathlib.Algebra.Algebra.Hom
import Mathlib.Algebra.Ring.Aut
/-!
# Isomorphisms of `R`-algebras
This file defines bundled isomorphisms of `R`-algebras.... |
Algebra\Algebra\Field.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Yury Kudryashov
-/
import Mathlib.Algebra.Algebra.Defs
import Mathlib.Data.Rat.Cast.Defs
/-!
# Facts about `algebraMap` when the coefficient ring is a field.
-/
namespace algeb... |
Algebra\Algebra\Hom.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Yury Kudryashov
-/
import Mathlib.Algebra.Algebra.Basic
import Mathlib.Algebra.BigOperators.Finsupp
/-!
# Homomorphisms of `R`-algebras
This file defines bundled homomorphisms ... |
Algebra\Algebra\NonUnitalHom.lean | /-
Copyright (c) 2021 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.Algebra.Algebra.Hom
import Mathlib.Algebra.GroupWithZero.Action.Prod
/-!
# Morphisms of non-unital algebras
This file defines morphisms between two types, ... |
Algebra\Algebra\NonUnitalSubalgebra.lean | /-
Copyright (c) 2023 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Algebra.Algebra.NonUnitalHom
import Mathlib.Data.Set.UnionLift
import Mathlib.LinearAlgebra.Span
import Mathlib.RingTheory.NonUnitalSubring.Basic
/-!
# ... |
Algebra\Algebra\Operations.lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import Mathlib.Algebra.Algebra.Bilinear
import Mathlib.Algebra.Algebra.Equiv
import Mathlib.Algebra.Algebra.Opposite
import Mathlib.Algebra.GroupWithZero.NonZeroDivisors
import... |
Algebra\Algebra\Opposite.lean | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.Algebra.Equiv
import Mathlib.Algebra.Module.Opposites
import Mathlib.Algebra.Ring.Opposite
/-!
# Algebra structures on the multiplicative opposite
... |
Algebra\Algebra\Pi.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Yury Kudryashov
-/
import Mathlib.Algebra.Algebra.Equiv
/-!
# The R-algebra structure on families of R-algebras
The R-algebra structure on `∀ i : I, A i` when each `A i` is an ... |
Algebra\Algebra\Prod.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Yury Kudryashov
-/
import Mathlib.Algebra.Algebra.Hom
import Mathlib.Algebra.Module.Prod
/-!
# The R-algebra structure on products of R-algebras
The R-algebra structure on `(i ... |
Algebra\Algebra\Quasispectrum.lean | /-
Copyright (c) 2024 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Algebra.Algebra.Unitization
import Mathlib.Algebra.Algebra.Spectrum
/-!
# Quasiregularity and quasispectrum
For a non-unital ring `R`, an element `r : ... |
Algebra\Algebra\Rat.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Yury Kudryashov
-/
import Mathlib.Data.Rat.Cast.CharZero
import Mathlib.Algebra.Algebra.Defs
/-!
# Further basic results about `Algebra`'s over `ℚ`.
This file could usefully be... |
Algebra\Algebra\RestrictScalars.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Yury Kudryashov
-/
import Mathlib.Algebra.Algebra.Tower
/-!
# The `RestrictScalars` type alias
See the documentation attached to the `RestrictScalars` definition for advice on... |
Algebra\Algebra\Spectrum.lean | /-
Copyright (c) 2021 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Algebra.Star.Subalgebra
import Mathlib.RingTheory.Ideal.Maps
import Mathlib.Tactic.NoncommRing
/-!
# Spectrum of an element in an algebra
This file deve... |
Algebra\Algebra\Tower.lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Anne Baanen
-/
import Mathlib.Algebra.Algebra.Equiv
import Mathlib.LinearAlgebra.Span
/-!
# Towers of algebras
In this file we prove basic facts about towers of algebra.
An al... |
Algebra\Algebra\Unitization.lean | /-
Copyright (c) 2022 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Algebra.Algebra.Defs
import Mathlib.Algebra.Algebra.NonUnitalHom
import Mathlib.Algebra.Star.Module
import Mathlib.Algebra.Star.NonUnitalSubalgebra
impor... |
Algebra\Algebra\Hom\Rat.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Yury Kudryashov
-/
import Mathlib.Algebra.Algebra.Hom
import Mathlib.Algebra.Algebra.Rat
/-!
# Homomorphisms of `ℚ`-algebras
-/
namespace RingHom
variable {R S : Type*}
/--... |
Algebra\Algebra\Subalgebra\Basic.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Yury Kudryashov
-/
import Mathlib.Algebra.Algebra.Operations
/-!
# Subalgebras over Commutative Semiring
In this file we define `Subalgebra`s and the usual operations on them (... |
Algebra\Algebra\Subalgebra\Directed.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.Algebra.Algebra.Subalgebra.Basic
import Mathlib.Data.Set.UnionLift
/-!
# Subalgebras and directed Unions of sets
## Main results
* `Subalgebra.coe_iSup_o... |
Algebra\Algebra\Subalgebra\MulOpposite.lean | /-
Copyright (c) 2024 Jz Pan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jz Pan
-/
import Mathlib.Algebra.Ring.Subring.MulOpposite
import Mathlib.Algebra.Algebra.Subalgebra.Basic
/-!
# Subalgebras of opposite rings
For every ring `A` over a commutative ring `R`,... |
Algebra\Algebra\Subalgebra\Operations.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang, Antoine Chambert-Loir
-/
import Mathlib.Algebra.Algebra.Subalgebra.Basic
import Mathlib.RingTheory.Ideal.Maps
/-!
# More operations on subalgebras
In this file we relate the ... |
Algebra\Algebra\Subalgebra\Order.lean | /-
Copyright (c) 2021 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
import Mathlib.Algebra.Algebra.Subalgebra.Basic
import Mathlib.Algebra.Module.Submodule.Order
import Mathlib.Algebra.Ring.Subsemiring.Order
import Mathlib.Algebra.Ring... |
Algebra\Algebra\Subalgebra\Pointwise.lean | /-
Copyright (c) 2021 Eric Weiser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.Algebra.Operations
import Mathlib.Algebra.Algebra.Subalgebra.Basic
import Mathlib.Algebra.Ring.Subring.Pointwise
import Mathlib.RingTheory.Adjoin.Bas... |
Algebra\Algebra\Subalgebra\Prod.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca
-/
import Mathlib.Algebra.Algebra.Prod
import Mathlib.Algebra.Algebra.Subalgebra.Basic
/-!
# Products of subalgebras
In this file we define the product of two subalgebras ... |
Algebra\Algebra\Subalgebra\Rank.lean | /-
Copyright (c) 2024 Jz Pan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jz Pan
-/
import Mathlib.LinearAlgebra.Dimension.Free
import Mathlib.LinearAlgebra.Dimension.Finite
import Mathlib.LinearAlgebra.FreeModule.StrongRankCondition
/-!
# Some results on the rank... |
Algebra\Algebra\Subalgebra\Tower.lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Anne Baanen
-/
import Mathlib.Algebra.Algebra.Subalgebra.Basic
import Mathlib.Algebra.Algebra.Tower
/-!
# Subalgebras in towers of algebras
In this file we prove facts about su... |
Algebra\Algebra\Subalgebra\Unitization.lean | /-
Copyright (c) 2023 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Algebra.Algebra.Unitization
import Mathlib.Algebra.Star.NonUnitalSubalgebra
import Mathlib.Algebra.Star.Subalgebra
import Mathlib.GroupTheory.GroupAction... |
Algebra\Associated\Basic.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jens Wagemaker
-/
import Mathlib.Algebra.Group.Even
import Mathlib.Algebra.GroupWithZero.Divisibility
import Mathlib.Algebra.GroupWithZero.Hom
import Mathlib.Algebra.Gr... |
Algebra\Associated\OrderedCommMonoid.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jens Wagemaker
-/
import Mathlib.Algebra.Associated.Basic
import Mathlib.Algebra.Order.Monoid.Canonical.Defs
/-!
# Associated, prime, and irreducible elements.
In thi... |
Algebra\BigOperators\Associated.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jens Wagemaker, Anne Baanen
-/
import Mathlib.Algebra.Associated.Basic
import Mathlib.Algebra.BigOperators.Finsupp
/-!
# Products of associated, prime, and irreducible... |
Algebra\BigOperators\Fin.lean | /-
Copyright (c) 2020 Yury Kudryashov, Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Anne Baanen
-/
import Mathlib.Algebra.BigOperators.Ring
import Mathlib.Algebra.Group.Action.Pi
import Mathlib.Data.Fintype.BigOperators
import Mathlib.Da... |
Algebra\BigOperators\Finprod.lean | /-
Copyright (c) 2020 Kexing Ying and Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying, Kevin Buzzard, Yury Kudryashov
-/
import Mathlib.Algebra.BigOperators.GroupWithZero.Finset
import Mathlib.Algebra.Group.FiniteSupport
import Mathlib.Algebra... |
Algebra\BigOperators\Finsupp.lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import Mathlib.Algebra.BigOperators.Pi
import Mathlib.Algebra.BigOperators.Ring
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Algebra.Group.Submonoid.Membership
import... |
Algebra\BigOperators\Intervals.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.Algebra.BigOperators.Group.Finset
import Mathlib.Algebra.Order.Interval.Finset
import Mathlib.Order.Interval.Finset.Nat
import Mathlib.Tactic.Linarith
... |
Algebra\BigOperators\Module.lean | /-
Copyright (c) 2022 Dylan MacKenzie. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dylan MacKenzie
-/
import Mathlib.Algebra.BigOperators.Intervals
import Mathlib.Algebra.Module.Defs
import Mathlib.Tactic.Abel
/-!
# Summation by parts
-/
namespace Finset
variable ... |
Algebra\BigOperators\NatAntidiagonal.lean | /-
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import Mathlib.Algebra.BigOperators.Group.Finset
import Mathlib.Data.Finset.NatAntidiagonal
/-!
# Big operators for `NatAntidiagonal`
This file contains theorems re... |
Algebra\BigOperators\Option.lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Algebra.BigOperators.Group.Finset
import Mathlib.Data.Finset.Option
/-!
# Lemmas about products and sums over finite sets in `Option α`
In this fil... |
Algebra\BigOperators\Pi.lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Patrick Massot
-/
import Mathlib.Algebra.BigOperators.Group.Finset
import Mathlib.Algebra.Group.Action.Pi
import Mathlib.Algebra.Ring.Pi
/-!
# Big operators for Pi Types
Th... |
Algebra\BigOperators\Ring.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.Algebra.BigOperators.GroupWithZero.Finset
import Mathlib.Algebra.BigOperators.Ring.Multiset
import Mathlib.Algebra.Field.Defs
import Mathlib.Data.Finty... |
Algebra\BigOperators\RingEquiv.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Callum Sutton, Yury Kudryashov
-/
import Mathlib.Algebra.BigOperators.Group.Finset
import Mathlib.Algebra.Ring.Equiv
import Mathlib.Algebra.Ring.Opposite
/-!
# Results... |
Algebra\BigOperators\WithTop.lean | /-
Copyright (c) 2024 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Yaël Dillies
-/
import Mathlib.Algebra.BigOperators.Group.Finset
import Mathlib.Algebra.Order.Ring.WithTop
/-!
# Sums in `WithTop`
This file proves results about finite... |
Algebra\BigOperators\Group\Finset.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.Algebra.Group.Indicator
import Mathlib.Data.Finset.Piecewise
import Mathlib.Data.Finset.Preimage
import Mathlib.Data.Finset.Sym
import Mathlib.Data.Sym... |
Algebra\BigOperators\Group\List.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Floris van Doorn, Sébastien Gouëzel, Alex J. Best
-/
import Mathlib.Algebra.Divisibility.Basic
import Mathlib.Algebra.Group.Int
import Mathlib.Algebra.Group.Nat
import ... |
Algebra\BigOperators\Group\Multiset.lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Algebra.BigOperators.Group.List
import Mathlib.Algebra.Group.Prod
import Mathlib.Data.Multiset.Basic
/-!
# Sums and products over multisets
In... |
Algebra\BigOperators\GroupWithZero\Finset.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.Algebra.BigOperators.Group.Finset
import Mathlib.Algebra.GroupWithZero.Units.Basic
/-!
# Big operators on a finset in groups with zero
This file cont... |
Algebra\BigOperators\Ring\List.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Floris van Doorn, Sébastien Gouëzel, Alex J. Best
-/
import Mathlib.Algebra.BigOperators.Group.List
import Mathlib.Algebra.GroupWithZero.Commute
import Mathlib.Algebra.... |
Algebra\BigOperators\Ring\Multiset.lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Bhavik Mehta, Eric Wieser
-/
import Mathlib.Algebra.BigOperators.Group.Multiset
import Mathlib.Algebra.BigOperators.Ring.List
import Mathlib.Data.Multiset.Antidiagonal
impo... |
Algebra\BigOperators\Ring\Nat.lean | /-
Copyright (c) 2024 Pim Otte. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Pim Otte
-/
import Mathlib.Algebra.BigOperators.Group.Finset
import Mathlib.Algebra.Ring.Parity
/-!
# Big operators on a finset in the natural numbers
This file contains the results concer... |
Algebra\Category\BoolRing.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Algebra.Category.Ring.Basic
import Mathlib.Algebra.Ring.BooleanRing
import Mathlib.Order.Category.BoolAlg
/-!
# The category of Boolean rings
This file d... |
Algebra\Category\GrpWithZero.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Algebra.Category.MonCat.Basic
import Mathlib.Algebra.GroupWithZero.WithZero
import Mathlib.CategoryTheory.Category.Bipointed
/-!
# The category of groups ... |
Algebra\Category\AlgebraCat\Basic.lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.Algebra.Algebra.Subalgebra.Basic
import Mathlib.Algebra.FreeAlgebra
import Mathlib.Algebra.Category.Ring.Basic
import Mathlib.Algebra.Category.ModuleCa... |
Algebra\Category\AlgebraCat\Limits.lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.Algebra.Category.AlgebraCat.Basic
import Mathlib.Algebra.Category.ModuleCat.Basic
import Mathlib.Algebra.Category.ModuleCat.Limits
import Mathlib.Algeb... |
Algebra\Category\AlgebraCat\Monoidal.lean | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.CategoryTheory.Monoidal.Transport
import Mathlib.Algebra.Category.AlgebraCat.Basic
import Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic
import Mathlib.Ri... |
Algebra\Category\AlgebraCat\Symmetric.lean | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.Category.AlgebraCat.Monoidal
import Mathlib.Algebra.Category.ModuleCat.Monoidal.Symmetric
/-!
# The monoidal structure on `AlgebraCat` is symmetric.... |
Algebra\Category\BialgebraCat\Basic.lean | /-
Copyright (c) 2024 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
import Mathlib.Algebra.Category.CoalgebraCat.Basic
import Mathlib.Algebra.Category.AlgebraCat.Basic
import Mathlib.RingTheory.Bialgebra.Equiv
/-!
# The categor... |
Algebra\Category\CoalgebraCat\Basic.lean | /-
Copyright (c) 2024 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
import Mathlib.Algebra.Category.ModuleCat.Basic
import Mathlib.RingTheory.Coalgebra.Equiv
/-!
# The category of coalgebras over a commutative ring
We introduc... |
Algebra\Category\CoalgebraCat\ComonEquivalence.lean | /-
Copyright (c) 2024 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
import Mathlib.CategoryTheory.Monoidal.Braided.Opposite
import Mathlib.Algebra.Category.ModuleCat.Monoidal.Symmetric
import Mathlib.CategoryTheory.Monoidal.Como... |
Algebra\Category\FGModuleCat\Basic.lean | /-
Copyright (c) 2021 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer
-/
import Mathlib.CategoryTheory.Monoidal.Rigid.Basic
import Mathlib.CategoryTheory.Monoidal.Subcategory
import Mathlib.LinearAlgebra.Coevaluation
import Mathlib.Lin... |
Algebra\Category\FGModuleCat\Limits.lean | /-
Copyright (c) 2022 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.Algebra.Category.FGModuleCat.Basic
import Mathlib.Algebra.Category.ModuleCat.Limits
import Mathlib.Algebra.Category.ModuleCat.Products
import Mathlib.A... |
Algebra\Category\Grp\AB5.lean | /-
Copyright (c) 2023 David Kurniadi Angdinata. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Kurniadi Angdinata, Moritz Firsching, Nikolas Kuhn, Amelia Livingston
-/
import Mathlib.Algebra.Homology.ShortComplex.Ab
import Mathlib.Algebra.Homology.ShortComplex.E... |
Algebra\Category\Grp\Abelian.lean | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import Mathlib.Algebra.Category.Grp.Colimits
import Mathlib.Algebra.Category.Grp.Limits
import Mathlib.Algebra.Category.Grp.ZModuleEquivalence
import Mathlib.Algebra.Ca... |
Algebra\Category\Grp\Adjunctions.lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Johannes Hölzl
-/
import Mathlib.Algebra.Category.Grp.Preadditive
import Mathlib.GroupTheory.FreeAbelianGroup
import Mathlib.CategoryTheory.Limits.Shapes.Types
/-!
# A... |
Algebra\Category\Grp\Basic.lean | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.Algebra.Category.MonCat.Basic
import Mathlib.Algebra.Group.ULift
import Mathlib.CategoryTheory.Endomorphism
import Mathlib.Data.Int.Cast.Lemmas
import ... |
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