Theorems · Theorem · commutative algebra
Algebra.FormallyUnramified.of_isLocalization
∀ {R : Type u_1} {Rₘ : Type u_3} [inst : CommRing R] [inst_1 : CommRing Rₘ] (M : Submonoid R) [inst_2 : Algebra R Rₘ]
[IsLocalization M Rₘ], Algebra.FormallyUnramified R RₘThis holds in general for epimorphisms.
- Defined in
- Mathlib.RingTheory.Unramified.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Idealproof · cited by 4,748
- Bot.botproof · cited by 4,720
- Algebra.algebraMapproof · cited by 4,706
- AlgHomproof · cited by 3,236
- Submonoidstatement and proof · cited by 3,086
- IsLocalizationstatement and proof · cited by 636
- AlgHom.compproof · cited by 501
- RingHom.extproof · cited by 331
- Ideal.Quotient.mkₐproof · cited by 101
Cited by5
Results whose statement or proof uses this declaration.
- Algebra.FormallyUnramified.isReduced_of_fieldproof · cited by 6
- Algebra.FormallyEtale.of_isLocalizationproof · cited by 3
- RingHom.FormallyUnramified.holdsForLocalizationproof · cited by 2
- Algebra.FormallyUnramified.localization_mapproof · cited by 0
- Algebra.Unramified.of_isLocalization_Awayproof · cited by 0