Theorems · Theorem · commutative algebra
IsLocalization.isLocalization_of_algEquiv
∀ {R : Type u_1} [inst : CommSemiring R] (M : Submonoid R) {S : Type u_2} [inst_1 : CommSemiring S]
[inst_2 : Algebra R S] {P : Type u_3} [inst_3 : CommSemiring P] [inst_4 : Algebra R P] [IsLocalization M S]
(h : S ≃ₐ[R] P), IsLocalization M P- Defined in
- Mathlib.RingTheory.Localization.Basic
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Algebra.algebraMapproof · cited by 4,706
- Monoidproof · cited by 3,887
- Submonoidstatement and proof · cited by 3,086
- AlgEquivstatement and proof · cited by 1,681
- IsUnitproof · cited by 1,602
- map_mulproof · cited by 1,137
- IsLocalizationstatement and proof · cited by 636
- AlgEquiv.symmproof · cited by 615
- AlgHom.toRingHomproof · cited by 490
Cited by11
Results whose statement or proof uses this declaration.
- Algebra.IsStandardOpenImmersion.of_algEquivproof · cited by 3
- RingHom.HoldsForLocalizationAway.of_bijectiveproof · cited by 2
- IsLocalization.isLocalization_iff_of_isLocalizationproof · cited by 2
- IsLocalization.selfproof · cited by 2
- IsFractionRing.self_iff_bijectiveproof · cited by 1
- IsLocalization.isLocalization_iff_of_algEquivproof · cited by 1
- IsFractionRing.of_algEquivproof · cited by 1
- IsFractionRing.transproof · cited by 0
- mem_adjoin_map_integralClosure_of_isStandardEtaleproof · cited by 0
- IsLocalization.adjoin_invproof · cited by 0
- RingHom.locally_holdsForLocalizationAwayproof · cited by 0