chars int64 40 24k | content_type stringclasses 9
values | id stringlengths 13 64 | source stringclasses 5
values | subset stringclasses 31
values | text stringlengths 40 24k |
|---|---|---|---|---|---|
11,251 | lean_file_chunk | 9ae3ea47ff6332abc1e1c7f4b35f88df48042b77c3e853e356e26f8afcf72fe6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
module
public import Mathlib.Condensed.Discrete.Colimit
public import Mathlib.Condensed.Discrete.Module
/-!
# Characterizing discrete condensed sets and `R`-mod... |
11,764 | lean_file_chunk | 4f9c59c7b1baef46ff4c952dd90faeba1083c040089f2d646f386658c5d7718d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
module
public import Mathlib.CategoryTheory.Sites.ConstantSheaf
public import Mathlib.Condensed.Discrete.LocallyConstant
public import Mathlib.Condensed.Light.Mo... |
3,638 | lean_file_chunk | 820b4754682b134a67c342778a38a8c1ad60982f4ca81c931dadd76a99e6b88f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
module
public import Mathlib.CategoryTheory.Sites.ConstantSheaf
public import Mathlib.CategoryTheory.Sites.Equivalence
public import Mathlib.Condensed.Basic
publ... |
19,313 | lean_file_chunk | 501297f9442d4e8b504ac866b8e7db31c59661b09d109d8c57896d812ee0bb96 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
module
public import Mathlib.Condensed.Discrete.Basic
public import Mathlib.Condensed.TopComparison
public import Mathlib.Topology.Category.CompHausLike.SigmaCom... |
1,494 | lean_file_chunk | 94cf34a31e9c82bdff8678ff3eccd53095d2cede0c8800831e9a97688fd67c44 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.Topology.Category.LightProfinite.EffectiveEpi
public import Mathlib.CategoryTheory.Sites.Equivalence
/-!
# `HasSheafify` instances
In this file,... |
3,218 | lean_file_chunk | 0e60010e2e5c98a07cbcfcdd6886541bb3bab339fb92a9b636b86b28b178023f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
module
public import Mathlib.Algebra.Category.ModuleCat.Abelian
public import Mathlib.Algebra.Category.ModuleCat.Adjunctions
public import Mathlib.Algebra.Catego... |
2,447 | lean_file_chunk | 78a53b7351b267febe7fa42670f654d4a0ebe5bd9d48cdeaab779e65d05622ec | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
module
public import Mathlib.Algebra.Category.ModuleCat.Monoidal.Closed
public import Mathlib.CategoryTheory.Monoidal.Braided.Reflection
public import Mathlib.Ca... |
1,083 | lean_file_chunk | 56013583a768f397e546ce137a9ea82e48047106b590c2a6250e0ab0fcfa14d8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Jonas van der Schaaf. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jonas van der Schaaf, Dagur Asgeirsson
-/
module
public import Mathlib.CategoryTheory.Sites.RegularEpi
public import Mathlib.Condensed.Light.Epi
public import Mathlib.Condensed.... |
3,387 | lean_file_chunk | 3579e2359f303c29d68e3b72f5ac8807fd24d548cbb78ab8810511d42037f7d8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
module
public import Mathlib.CategoryTheory.Sites.CartesianMonoidal
public import Mathlib.CategoryTheory.Sites.PreservesLimits
public import Mathlib.Condensed.Li... |
17,290 | lean_file_chunk | e3e36ef7514f98ef76504c80a752c109e9926bc377d6b85e7124995534082543 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Jonas van der Schaaf. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jonas van der Schaaf, Dagur Asgeirsson
-/
module
public import Mathlib.Condensed.Light.InternallyProjective
import Mathlib.Condensed.Light.EffectiveEpi
import Mathlib.Topology.... |
2,102 | lean_file_chunk | bfa055a2435891e47c4fe448a2418396504516a8aa562e3ed7cf95ac50696982 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
module
public import Mathlib.CategoryTheory.Sites.Sheaf
public import Mathlib.Topology.Category.LightProfinite.EffectiveEpi
/-!
# Light condensed objects
This ... |
13,714 | lean_file_chunk | 8fea999c25c743bd78524fdf2217384f8084bf061f84cad10d534f8908d050a2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
module
public import Mathlib.CategoryTheory.Preadditive.Projective.Internal
public import Mathlib.Condensed.Light.Epi
public import Mathlib.Condensed.Light.Funct... |
1,013 | lean_file_chunk | 6559fe5820ceed396c1f2aa5ba95c2db0733077b99608301f89fca9b87f95888 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
module
public import Mathlib.Condensed.Light.Basic
public import Mathlib.Condensed.TopComparison
/-!
# The functor from topological spaces to light condensed s... |
473 | lean_file_chunk | cec570c02141b266d4bfc277a0628eb9f31e73489fb1f0e2d4f4147a08687efc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
module
public import Mathlib.CategoryTheory.Monoidal.Closed.Types
public import Mathlib.CategoryTheory.Sites.CartesianClosed
public import Mathlib.CategoryTheory... |
3,996 | lean_file_chunk | 45584e732f63a3af7027842787397bfb98b53461c47495ec73cbbd082df9ac4a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
module
public import Mathlib.CategoryTheory.Sites.Coherent.SheafComparison
public import Mathlib.Condensed.Light.Module
/-!
# The explicit sheaf condition for l... |
8,673 | lean_file_chunk | 8ce384fee80dde983c5882698aeacd69355126099cdabdf8d9589b09b764b09b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
module
public import Mathlib.Condensed.Light.TopComparison
public import Mathlib.Topology.Category.Sequential
public import Mathlib.Topology.Category.LightProfin... |
2,791 | lean_file_chunk | 142787988db89d2de93bcd8e36a04ee00dbf489f71d81537cba31868e316f525 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
module
public import Mathlib.CategoryTheory.Sites.Equivalence
public import Mathlib.Condensed.Light.Module
/-!
# Equivalence of light condensed objects with sh... |
6,236 | lean_file_chunk | fc5743c606a12bf37c4abbcdc793799109c62be3396fe8db4f979794ef7ca436 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.SequentialProduct
public import Mathlib.CategoryTheory.Sites.Coherent.SequentialLimit
public import Mat... |
1,021 | lean_file_chunk | 35476cb59b805325006ef8aeacd42d827c142b4379998677ebd31cfa88e8cf9d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
module
public import Mathlib.Algebra.Category.ModuleCat.AB
public import Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Sheaf
public import Mathlib.Condensed.... |
503 | lean_file_chunk | c53def606772910aee90889d5e89cc8a1b46bba18dc95c41fab17017fa5115d5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
module
public import Mathlib.Condensed.Light.Module
/-!
# Limits in categories of light condensed objects
This file adds some instances for limits in light con... |
595 | lean_file_chunk | ed215d116942358c3d11bb440df0107f3781052a117379960e93ac305f05a534 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
module
public import Mathlib.LinearAlgebra.Matrix.Ideal
public import Mathlib.RingTheory.SimpleRing.Basic
/-!
The matrix ring over a simple ring is simple
-/
@[expose]... |
3,793 | lean_file_chunk | d51fc6271e11fc737da54e4d938f9fea701ee42b50a14062363d09b0c032f040 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
module
public import Mathlib.RingTheory.SimpleRing.Defs
public import Mathlib.Algebra.Ring.Opposite
public import Mathlib.RingTheory.TwoSidedIdeal.Kernel
/-! # Basic Pr... |
1,543 | lean_file_chunk | d50eb3a4195358e9204b82ed6ca5312270bd82be0332d2675d070d3df897cfa8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
module
public import Mathlib.RingTheory.SimpleRing.Basic
public import Mathlib.RingTheory.TwoSidedIdeal.Operations
/-!
# Simplicity is preserved by ring isomorphisms/su... |
711 | lean_file_chunk | 98ea1bb7ba35894fba5ae73d65c080337fd9da4c3eee82cb1a089c2c6f9b09cb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
module
public import Mathlib.RingTheory.TwoSidedIdeal.Lattice
public import Mathlib.Order.Atoms
/-! # Simple rings
A ring `R` is **simple** if it has only two two-side... |
2,264 | lean_file_chunk | 1a942e306d5c6024a1377ede72003dfa5cc799b2df6d5fc4b5d57318bd6ff9dc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
module
public import Mathlib.RingTheory.SimpleRing.Basic
public import Mathlib.Algebra.Ring.Subring.Basic
public import Mathlib.Algebra.Field.Equiv
/-!
# Simple ring an... |
822 | lean_file_chunk | 2652c9f4ce1e154aca5e7aae604a883543beb4088997eed516cf7d8720883fa8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
module
public import Mathlib.RingTheory.PrincipalIdealDomain
public import Mathlib.RingTheory.SimpleRing.Field
public import Mathlib.RingTheory.TwoSidedIdeal.Opera... |
5,260 | lean_file_chunk | c9fdad034b6225c30fa26185f4be177dcc82ffadf923f24fb8ed4e62e5214ca9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Arend Mellendijk, Jeremy Tan
-/
module
public import Mathlib.Algebra.EuclideanDomain.Int
public import Mathlib.Algebra.GCDMonoid.Nat
public import Mathlib.Data.Nat.Prime.I... |
16,108 | lean_file_chunk | b0ac7955daf2b0d15617d41a49e6c4c1112e8e46694e59bd4f5523ac36d02153 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jineon Baek, Seewoo Lee. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jineon Baek, Seewoo Lee, Bhavik Mehta, Arend Mellendijk
-/
module
public import Mathlib.Algebra.EuclideanDomain.Basic
public import Mathlib.Algebra.Order.Group.Finset
public ... |
23,949 | lean_file_chunk | 3f0f0ee63da6637fba050ce549b629ef25536542f1f41542812c52a8c37efc3c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
module
public import Mathlib.Algebra.Group.Subgroup.Basic
public import Mathlib.Algebra.Group.Submonoid.BigOperators
public import Mathlib.GroupTheory.Subsemigroup.Cen... |
7,742 | lean_file_chunk | 031e8b4c80744cd9b6360e31b92dc299261ee936e549122067359abb58154344 | lean_source_file | pkg_mathlib_source_file_chunks | theorem prod_mono_left (t : NonUnitalSubring S) : Monotone fun s : NonUnitalSubring R => s.prod t :=
fun _s₁ _s₂ hs => prod_mono hs (le_refl t)
theorem prod_top (s : NonUnitalSubring R) :
s.prod (⊤ : NonUnitalSubring S) = s.comap (NonUnitalRingHom.fst R S) :=
ext fun x => by simp [mem_prod]
theorem top_prod (... |
13,083 | lean_file_chunk | 811b217ef8ac2493379603b110e4b185fac8c443b8eb7741ae94f63864e79e5a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
module
public import Mathlib.Algebra.Group.Subgroup.Defs
public import Mathlib.RingTheory.NonUnitalSubsemiring.Defs
public import Mathlib.Tactic.FastInstance
/-!
# `N... |
6,071 | lean_file_chunk | 6c31b1f23d3949edf009ebf63cf30a65f0443c14d2658ac0bd35b1f4967b3412 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Matthew Jasper. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Matthew Jasper, Kevin Buzzard
-/
module
public import Mathlib.Algebra.Module.Torsion.Basic
public import Mathlib.RingTheory.DedekindDomain.Dvr
public import Mathlib.RingTheory.Flat.Lo... |
14,549 | lean_file_chunk | 79d7d917d084f6890e5cfae4152c28c6f548cb99d0f682cdc4416be5ccaeaf71 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Mitchell Lee. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mitchell Lee, Junyan Xu
-/
module
public import Mathlib.Algebra.Module.FinitePresentation
public import Mathlib.LinearAlgebra.TensorProduct.Vanishing
public import Mathlib.RingTheory.Fl... |
5,504 | lean_file_chunk | 561b8141c86183427996843e22541ad04210172479aac9fb01707c583c34f82a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.LinearAlgebra.Trace
public import Mathlib.RingTheory.Spectrum.Prime.FreeLocus
/-!
# Results for the rank of a finite flat algebra
... |
23,972 | lean_file_chunk | ad36d0817300951956cfdc7988c0b4a3039456bccb969728df980deade04366f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Jujian Zhang, Yongle Hu
-/
module
public import Mathlib.Algebra.Colimit.TensorProduct
public import Mathlib.Algebra.Module.Projective
public import Mathlib.LinearAlgeb... |
7,837 | lean_file_chunk | 372e1bd8492a706410a61d204cd4543819d118dfb51f3f2b70dbaec6235cb85e | lean_source_file | pkg_mathlib_source_file_chunks | simp [finsuppTensorFinsupp'_symm_single_eq_single_one_tmul]
/-- Tensor product of linearly independent families is linearly
independent under some flatness conditions.
The flatness condition could be removed over domains.
See `LinearIndepOn.tmul_of_isDomain`. -/
nonrec lemma LinearIndepOn.tmul_of_flat_left [Module.Fl... |
3,622 | lean_file_chunk | 912c480af98778e534777a4a89b7253f785a37070d89025375e8b8ca9fe021c7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.LinearAlgebra.Basis.VectorSpace
public import Mathlib.RingTheory.Flat.Localization
/-!
# Flat modules in domains
We show that the tensor pro... |
5,231 | lean_file_chunk | d0dd0e0e0d5de8b11fa296d737e215b278acfffc9c7c05496a4e943e9dc64fa5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junyan Xu
-/
module
public import Mathlib.RingTheory.Flat.Stability
public import Mathlib.RingTheory.LocalProperties.Exactness
/-!
# Flatness and localization
In this file we show that l... |
4,361 | lean_file_chunk | 762801b80fd7f8596a77887753401580353dc56f84185d2e2772fdf509273597 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.RingTheory.Flat.Basic
public import Mathlib.RingTheory.IsTensorProduct
public import Mathlib.LinearAlgebra.TensorProduct.Tower
publi... |
3,056 | lean_file_chunk | 3525a992d87843a00488124f5ca8096d4fe513e6f395c405bb228106c85f68a8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
module
public import Mathlib.RingTheory.Flat.Basic
public import Mathlib.Algebra.Homology.ShortComplex.ModuleCat
public import Mathlib.Algebra.Category.ModuleCat.Monoida... |
15,306 | lean_file_chunk | 8522d2d331502d02ca3fd7cf2cdd78dfeeaf6d9861c158adf69e8a0e6b817efb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.RingTheory.Flat.Basic
public import Mathlib.Algebra.Module.SnakeLemma
/-!
# Base change along flat modules preserves equalizers
We... |
4,493 | lean_file_chunk | 2c486e23872ef6aa05df0b336e0ff8887b6885bd58fbd3929ffd8886a660f7b3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Jujian Zhang
-/
module
public import Mathlib.Algebra.Module.CharacterModule
public import Mathlib.RingTheory.Flat.Basic
/-!
# Flat modules
`M` is flat if `· ⊗ M` pre... |
11,345 | lean_file_chunk | 4e2884c6dbeb70710a0811c5f0e881c5c92a6f40187910c130159c7144d66d99 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Nailin Guan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nailin Guan, Yongle Hu
-/
module
public import Mathlib.RingTheory.Flat.TorsionFree
public import Mathlib.RingTheory.KrullDimension.Module
public import Mathlib.RingTheory.Regular.Regular... |
3,936 | lean_file_chunk | b4a013927533d93f4aa482e0f29c61ed55673ad98ea35c73c50ea5f4adf64db4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Nailin Guan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nailin Guan
-/
module
public import Mathlib.RingTheory.KrullDimension.NonZeroDivisors
public import Mathlib.RingTheory.Spectrum.Prime.Module
/-!
# Krull Dimension of Module
In this fi... |
2,073 | lean_file_chunk | e4a9a748d77a28f7e9f7a71f1e3e816d3db19a1da3b4d6fbcf182543e27073e9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Jingting Wang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jingting Wang
-/
module
public import Mathlib.RingTheory.LocalRing.MaximalIdeal.Basic
public import Mathlib.RingTheory.KrullDimension.Field
public import Mathlib.RingTheory.KrullDimens... |
2,549 | lean_file_chunk | 6a48a03ab5e8a9bfa9cf1da796fc1d4e58cfe7d7c55a1a7ebc388e51169eeec8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Jingting Wang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jingting Wang
-/
module
public import Mathlib.RingTheory.Ideal.Height
public import Mathlib.RingTheory.KrullDimension.Zero
public import Mathlib.RingTheory.PrincipalIdealDomain
/-!
# ... |
7,663 | lean_file_chunk | 614dfd9d9eb786fabf174500a19c0f7fb2dd9fdb540a14b11fba4c7ebc253bb4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fangming Li, Jujian Zhang
-/
module
public import Mathlib.Algebra.MvPolynomial.Basic -- shake: keep (used in `proof_wanted` only)
public import Mathlib.Order.KrullDimension
public impo... |
5,349 | lean_file_chunk | 586690c174525f29751b00ef2126b953a27c719c7adb171ce966ff67dc69c78a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.RingTheory.Ideal.MinimalPrime.Localization
public import Mathlib.RingTheory.KrullDimension.Basic
public import Mathlib.RingTheory.MvPowerSerie... |
665 | lean_file_chunk | 243d93db4f00791363c92945a1f0129cc3b256997a1fac7567a29aac81c0f97b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fangming Li, Jujian Zhang
-/
module
public import Mathlib.RingTheory.KrullDimension.Basic
/-!
# The Krull dimension of a field
This file proves that the Krull dimension of a field is ... |
6,169 | lean_file_chunk | 923a16c9db72c214dfec4773c6e64f296397258d0685c5f4d6690fb8fe2f45c9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Jingting Wang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jingting Wang, Sihan Su, Yi Song, Christian Merten
-/
module
public import Mathlib.Algebra.Polynomial.FieldDivision
public import Mathlib.RingTheory.KrullDimension.PID
public import Ma... |
7,168 | lean_file_chunk | 27b21fc75ea1f479b089229529cdb858e508cc193926fa2c982e6dc284d9c5c5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.RingTheory.Jacobson.Ring
public import Mathlib.RingTheory.Spectrum.Prime.Topology
/-!
# Zero-dimensional rings
We provide further API for z... |
21,446 | lean_file_chunk | 7451d2a8fa0d75a5abd09a4841f184714b319b3adf21997df2afe6f92d288c4d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.RingTheory.Extension.Cotangent.Basic
public import Mathlib.RingTheory.Extension.Generators
public import Mathlib.Algebra.Module.SnakeLemma
/-... |
13,802 | lean_file_chunk | 6abc8e1c62bfddb8217678fb0d22b04a6645741abe69c658cdda389a8e6e61e9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.RingTheory.Kaehler.Basic
public import Mathlib.RingTheory.Localization.BaseChange
/-!
# Kähler differential module under base change
## Main... |
23,961 | lean_file_chunk | 8143ae31d842a4f02089291d232c8e8472d9214e82a6fec54e15de8430b97de3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Nicolò Cavalleri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolò Cavalleri, Andrew Yang
-/
module
public import Mathlib.RingTheory.Derivation.ToSquareZero
public import Mathlib.RingTheory.Ideal.Cotangent
public import Mathlib.RingTheory.Is... |
14,559 | lean_file_chunk | dd10542e23950847877986f4ca384dcbf2e91784ee964ec0fa46c8f8254db583 | lean_source_file | pkg_mathlib_source_file_chunks | map_smul' _ _ := KaehlerDifferential.kerTotal_mkQ_single_smul _ _ _ _ _
map_one_eq_zero' := KaehlerDifferential.kerTotal_mkQ_single_algebraMap_one _ _ _
leibniz' a b :=
(KaehlerDifferential.kerTotal_mkQ_single_mul _ _ _ _ _).trans
(by simp_rw [← Finsupp.smul_single_one _ (1 * _ : S)]; dsimp; simp)
theore... |
5,332 | lean_file_chunk | 921e5eec1d15f111cccb6863f3e71a3d867f6e6c4ec525ec2f233269c774884a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.RingTheory.Kaehler.Basic
public import Mathlib.Algebra.MvPolynomial.PDeriv
public import Mathlib.Algebra.Polynomial.Derivation
/-!
# The Kähl... |
2,294 | lean_file_chunk | 715f1dcf6b63f75abfe6ea56fe2494c23e949da388afaecdd181ae4f42ad7b15 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Jiedong Jiang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jiedong Jiang
-/
module
public import Mathlib.RingTheory.Teichmuller
/-!
# Untilt Function
In this file, we define the untilt function from the pretilt of a
`p`-adically complete rin... |
8,129 | lean_file_chunk | 7778524625363e236af23e46da0aa8da118a00de82078bccd8f505271cbcf30e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Jiedong Jiang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jiedong Jiang
-/
module
public import Mathlib.RingTheory.AdicCompletion.Functoriality
public import Mathlib.RingTheory.AdicCompletion.RingHom
public import Mathlib.RingTheory.Perfectoi... |
3,453 | lean_file_chunk | 2f9044a090e524bf19f130768a64497eb8134444bbaff84bc0f4bfd3cfba99e7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Jiedong Jiang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jiedong Jiang
-/
module
public import Mathlib.RingTheory.AdicCompletion.Algebra
public import Mathlib.RingTheory.Localization.Away.Basic
public import Mathlib.RingTheory.Perfectoid.Fon... |
12,619 | lean_file_chunk | d4846f7e12f4391a58e1253062b451ff594b2aeb03a9d81c385c803edd069130 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Raphael Douglas Giles. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Raphael Douglas Giles
-/
module
public import Mathlib.RingTheory.KrullDimension.NonZeroDivisors
public import Mathlib.RingTheory.Length
public import Mathlib.RingTheory.Hopkins... |
9,355 | lean_file_chunk | 4c55ca4c8e92fb0dc2bf476572f45cc0eaa3f1230a2f195a45149207eff21f9a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Raphael Douglas Giles. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Raphael Douglas Giles
-/
module
public import Mathlib.RingTheory.KrullDimension.NonZeroDivisors
public import Mathlib.RingTheory.Length
public import Mathlib.RingTheory.OrderO... |
23,957 | lean_file_chunk | 91b2067f798d5935e19b2c3f2d58e416b01741e8e3d7e053b44445326e53caec | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
module
public import Mathlib.RingTheory.Invariant.Defs
public import Mathlib.RingTheory.IntegralClosure.IntegralRestrict
/-!
# Invariant Extensions of Rings
Give... |
1,475 | lean_file_chunk | 0153f114a6bf76dd8615cf95653dc93b753bb3ad5a383d77607cb86075ce51b1 | lean_source_file | pkg_mathlib_source_file_chunks | obtain ⟨x, rfl⟩ := Ideal.Quotient.mk_surjective x
cases nonempty_fintype G
obtain ⟨p, hp, h₁, h₂⟩ := Polynomial.lifts_and_degree_eq_and_monic
(Algebra.IsInvariant.charpoly_mem_lifts A B G x) (MulSemiringAction.monic_charpoly _ _)
have H : Polynomial.aeval x p = 0 := by
rw [Polynomial.aeval_def, ← Polynomi... |
1,169 | lean_file_chunk | 5f54b0db460a83a19af78c3a92ed3c54be85600583435753b12cdb853c9fc9a4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
module
public import Mathlib.Algebra.Algebra.Defs
/-!
# Invariant Extensions of Rings
Given an extension of rings `B/A` and an action of `G` on `B`, we introduce... |
9,102 | lean_file_chunk | af2f09a0185f2285658ae23e95a0c47bb8bbc4b5f1116694dcad6f311ab08a56 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.RingTheory.Invariant.Basic
public import Mathlib.Topology.Algebra.ClopenNhdofOne
public import Mathlib.Topology.Algebra.Category.ProfiniteGrp.... |
6,036 | lean_file_chunk | 564f058a36bbe16222f09e7b43e2164934bdd2f7c3fa88e83939b68a03efab0e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
module
public import Mathlib.RingTheory.Flat.FaithfullyFlat.Algebra
public import Mathlib.RingTheory.Length
/-!
# Lengths along extensions of local rings
This fi... |
21,814 | lean_file_chunk | 6a7613474770382a9ffccce81fd2e5d773fec071985cf1859fbbca4f4f78847b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.Algebra.Module.FinitePresentation
public import Mathlib.Algebra.Module.Torsion.Basic
public import Mathlib.RingTheory.FiniteType
public import... |
4,712 | lean_file_chunk | 5f52bee646b59a1c07faadeb1d85c24a282b2746ab8c0523d140615a76a591b7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Andrew Yang, Yaël Dillies, Javier López-Contreras. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang, Yaël Dillies, Javier López-Contreras
-/
module
public import Mathlib.Tactic.FieldSimp
public import Mathlib.RingTheory.LocalRing.RingHo... |
1,782 | lean_file_chunk | 270cf6f14e60f02da68d7a4fe8d79cf2ee43d789d7cb4450807a4f606b0da871 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Michal Staromiejski. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michal Staromiejski
-/
module
public import Mathlib.Algebra.Ring.Subsemiring.Basic
public import Mathlib.Algebra.GroupWithZero.NonZeroDivisors
public import Mathlib.RingTheory.Lo... |
4,108 | lean_file_chunk | 921eb095d9d977f983c731ecf25319aefec586dd49979e1cf05467ae2109c26f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Chris Hughes, Mario Carneiro
-/
module
public import Mathlib.RingTheory.LocalRing.Defs
public import Mathlib.RingTheory.Ideal.Nonunits
/-!
# Local rings
We prove basic proper... |
5,758 | lean_file_chunk | a9bb2b0ce7fd7718e5a4f250fb7fd5245a694833379f7e74a3b84ffd0a9c2f84 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang, Riccardo Brasca
-/
module
public import Mathlib.LinearAlgebra.Dimension.OrzechProperty
public import Mathlib.LinearAlgebra.FreeModule.PID
public import Mathlib.LinearAlg... |
4,271 | lean_file_chunk | 5122dd956ea7e7efd9bc6ba6cd6057739f49001e8102604cf0dc7746a7b61ec8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Michal Staromiejski. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michal Staromiejski
-/
module
public import Mathlib.Algebra.Ring.Pi
public import Mathlib.Algebra.Ring.Prod
public import Mathlib.RingTheory.LocalRing.MaximalIdeal.Basic
public i... |
1,233 | lean_file_chunk | 89edd3b979e8c13dbf9c3a9673ce93b5e00317404ea30b4e637dcc6ed020348b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Chris Hughes, Mario Carneiro
-/
module
public import Mathlib.Algebra.Group.Units.Defs
public import Mathlib.Algebra.Ring.Defs
/-!
# Local rings
Define local rings as commutat... |
11,215 | lean_file_chunk | d42ab32c96fd5061566e1fb36ad58b5b48ec77045a761b4648a2f19f99fa1d31 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Antoine Chambert-Loir & María Inés de Frutos—Fernández. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir, María Inés de Frutos—Fernández
-/
module
public import Mathlib.Algebra.RingQuot
public import Mathlib.RingTheory.Divided... |
23,991 | lean_file_chunk | 3616fc633161eff928ea77447b1e60b9585b86e6c49d63fbbafa6240920a0652 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
module
public import Mathlib.FieldTheory.Galois.Basic
public import Mathlib.FieldTheory.Minpoly.MinpolyDiv
public import Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure
p... |
1,787 | lean_file_chunk | c5dab5e79bfe0010baca362fc338ba1d58da6c298e577c122019536f15ec698d | lean_source_file | pkg_mathlib_source_file_chunks | (traceForm K L).dualBasis_involutive _ (traceForm_isSymm K)
theorem Module.Basis.traceDual_injective :
Function.Injective (Basis.traceDual : Basis ι K L → Basis ι K L) :=
(traceForm K L).dualBasis_injective _ (traceForm_isSymm K)
variable {K L b}
@[simp]
theorem Module.Basis.traceDual_inj {b' : Basis ι K L} :
... |
5,718 | lean_file_chunk | 330bb81bab59e3cc92169d2acd4618395f3379091e391336c1bb644e79c3e6b4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang, Riccardo Brasca
-/
module
public import Mathlib.RingTheory.DedekindDomain.Dvr
public import Mathlib.RingTheory.IntegralClosure.IntegralRestrict
public import Mathlib.Rin... |
7,099 | lean_file_chunk | 243100a1e9bbfd8f6838bd4c71ef17c768856263430799420fa2f60f20ac4b91 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
module
public import Mathlib.LinearAlgebra.FiniteDimensional.Lemmas
public import Mathlib.LinearAlgebra.Matrix.BilinearForm
public import Mathlib.LinearAlgebra.Trace
/-!
... |
19,904 | lean_file_chunk | 4c1c45639783abda3082322c621f6ef472d04d3aa6cd0fff081655178cd3879c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.LinearAlgebra.TensorProduct.RightExactness
public import Mathlib.RingTheory.Ideal.Cotangent
public import Mathlib.RingTheory.Localization.Defs... |
23,994 | lean_file_chunk | abdf29c6b7883a9da8740c4a37b0abdd99ceb90725b9d155f335b70759919f6e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.RingTheory.Ideal.Cotangent
public import Mathlib.RingTheory.Localization.Away.Basic
public import Mathlib.RingTheory.MvPolynomial.Tower
public... |
6,892 | lean_file_chunk | 74c9cc1eb703baeabc7f5c562c86bcab6743dba433fc09a76ca63d101b0e360f | lean_source_file | pkg_mathlib_source_file_chunks | ← ker_eq_ker_aeval_val]
lemma map_toComp_ker (Q : Generators S T ι') (P : Generators R S ι) :
P.ker.map (Q.toComp P).toAlgHom = RingHom.ker (Q.ofComp P).toAlgHom := by
letI : DecidableEq (ι' →₀ ℕ) := Classical.decEq _
apply le_antisymm
· rw [Ideal.map_le_iff_le_comap]
rintro x (hx : algebraMap P.Ring S x... |
23,980 | lean_file_chunk | 7ca8fbb54a3b37fc2c2983259ba85d4e7b11df09e1a581961653cab183d12298 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Antoine Chambert-Loir, María Inés de Frutos-Fernández. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir, María Inés de Frutos-Fernández
-/
module
public import Mathlib.RingTheory.DividedPowers.DPMorphism
public import Mathlib.... |
5,193 | lean_file_chunk | 1437b93cf17bc352163145e6b86c73b8b80a18034c9837407ea12ec0eeecc44b | lean_source_file | pkg_mathlib_source_file_chunks | /-- Divided powers on the codomain `B` of a surjective ring homomorphism `f` are compatible
with `f`. -/
theorem dpow_apply' (hIf : IsSubDPIdeal hI (RingHom.ker f ⊓ I)) {n : ℕ} {a : A} (ha : a ∈ I) :
dpow hI f n (f a) = f (hI.dpow n a) := by
classical
simp only [dpow, Function.extend_def]
have h : ∃ (a_1 : ... |
10,618 | lean_file_chunk | f1afc61c647076d96a939669daf7709234f7a18399be90ed32966fd4f85948f1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Antoine Chambert-Loir, María Inés de Frutos-Fernández. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir, María Inés de Frutos-Fernández
-/
module
public import Mathlib.RingTheory.DividedPowers.Basic
/-! # Divided power morphi... |
18,072 | lean_file_chunk | 781c0545e38fc5d1278b00824284d22b4e17859c09585efff3af741400b53080 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Antoine Chambert-Loir & María-Inés de Frutos—Fernández. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir, María-Inés de Frutos—Fernández
-/
module
public import Mathlib.RingTheory.PowerSeries.Basic
public import Mathlib.Combin... |
8,009 | lean_file_chunk | 01d007fc8c91dc2becd2594c3107631c76ea7c963a8761fe1e0af8d0d45d1448 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Antoine Chambert-Loir, María Inés de Frutos-Fernández. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir, María Inés de Frutos-Fernández
-/
module
public import Mathlib.NumberTheory.Padics.PadicIntegers
public import Mathlib.Ri... |
13,584 | lean_file_chunk | e89579fff1b56a39f21d525b9c01fd524e8f33aaebb4199df966a8e757289535 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Antoine Chambert-Loir, María Inés de Frutos-Fernández. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir, María Inés de Frutos-Fernández
-/
module
public import Mathlib.Data.Nat.Factorial.NatCast
public import Mathlib.RingTheor... |
4,693 | lean_file_chunk | 96d9fd86a74eb3644d4ef1206e1b9d3cfba11aa3f5d75f3174c98581483bf320 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Nailin Guan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nailin Guan
-/
module
public import Mathlib.Algebra.Module.Defs
public import Mathlib.Algebra.GradedMonoid
public import Mathlib.Algebra.Group.Submonoid.Defs
public import Mathlib.Algebr... |
5,050 | lean_file_chunk | da5e704566dedb660d9d2ccb28d57bc0bfad17404d7663f7b8eeda754c79143c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Jiedong Jiang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jiedong Jiang
-/
module
public import Mathlib.RingTheory.WittVector.Domain
public import Mathlib.RingTheory.WittVector.Truncated
public import Mathlib.RingTheory.WittVector.Teichmuller... |
17,557 | lean_file_chunk | 32e53a1338b2194541e06b9667d06fb81602d31ff2e0edb1aeee3937287f30bb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
-/
module
public import Mathlib.FieldTheory.Finite.Polynomial
public import Mathlib.NumberTheory.Basic
public import Mathlib.RingTheory.WittVector.Witt... |
10,250 | lean_file_chunk | bd23eab4a681d58a7982088b03c163323efaa72efe00fd5d7f1855235a54e712 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
-/
module
public import Mathlib.Algebra.CharP.Invertible
public import Mathlib.Algebra.MvPolynomial.Variables
public import Mathlib.Algebra.MvPolynomia... |
5,508 | lean_file_chunk | d6de88882051a19ce589664b864d4aecf47e3770d7d734709db7e42b84a0c2d0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Heather Macbeth, Johan Commelin
-/
module
public import Mathlib.RingTheory.WittVector.Domain
public import Mathlib.RingTheory.WittVector.MulCoeff
public import Mathl... |
5,334 | lean_file_chunk | c1a221f50b4966ebec71e296442eda2b1ef303a1f62e2be3c61ff16185077c29 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Jiedong Jiang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jiedong Jiang
-/
module
public import Mathlib.RingTheory.WittVector.Complete
public import Mathlib.RingTheory.WittVector.Teichmuller
/-!
# Teichmuller Series
Let `R` be a characteris... |
11,272 | lean_file_chunk | 3f776cf0bf51468fa285aed367953b28d43e3ee3e3db6fa31a8ad9a979ef225a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Heather Macbeth
-/
module
public import Mathlib.Algebra.MvPolynomial.Supported
public import Mathlib.RingTheory.WittVector.Truncated
/-!
# Leading terms of Witt vec... |
6,252 | lean_file_chunk | 44feb12f16957f538d19dbd67a145f589937fb4a9acd08154eb74faeb4322972 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
module
public import Mathlib.RingTheory.WittVector.Basic
public import Mathlib.RingTheory.WittVector.IsPoly
/-!
## The Verschiebung operator
## References
* [Haze... |
12,917 | lean_file_chunk | c0fcddccb2022fdfcb2ed672c12fc316820929e5165d5ad82aa74105c0737874 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
-/
module
public import Mathlib.Algebra.MvPolynomial.Counit
public import Mathlib.Algebra.MvPolynomial.Invertible
public import Mathlib.RingTheory.Witt... |
12,418 | lean_file_chunk | b1fdc344124d8c2c98b43eeb5362ffd682b8c6d3a4a87e9d6131ad7743bc344a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
module
public import Mathlib.Algebra.Algebra.ZMod
public import Mathlib.Data.Nat.Multiplicity
public import Mathlib.FieldTheory.Perfect
public import Mathlib.RingThe... |
7,992 | lean_file_chunk | e8004e5a20d4bf9f01f6c5022313c1e90a6ced516261e91393389a95272b20e0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
-/
module
public import Mathlib.RingTheory.WittVector.Truncated
public import Mathlib.RingTheory.WittVector.Identities
public import Mathlib.NumberTheo... |
7,679 | lean_file_chunk | be5ef95e7087bc5a08af7e848123ca29df63b1a8458eac3f958b7807d481e181 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Johan Commelin, Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
-/
module
public import Mathlib.RingTheory.WittVector.Basic
public import Mathlib.RingTheory.WittVector.IsPoly
/-!
# `init` and `tai... |
3,651 | lean_file_chunk | 66bba8754a87aec4d5fca3089554ca7ff9302fa1644473dafd99ad1ed64cde46 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis
-/
module
public import Mathlib.RingTheory.WittVector.Identities
/-!
# Witt vectors over a domain
This file builds to the proof `WittVector.instIsDomain`,
an insta... |
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