Theorems · Theorem · commutative algebra
IsLocalization.algEquiv_apply
∀ {R : Type u_1} [inst : CommSemiring R] (M : Submonoid R) (S : Type u_2) [inst_1 : CommSemiring S]
[inst_2 : Algebra R S] [inst_3 : IsLocalization M S] (Q : Type u_4) [inst_4 : CommSemiring Q] [inst_5 : Algebra R Q]
[inst_6 : IsLocalization M Q] (a : S), (IsLocalization.algEquiv M S Q) a = (IsLocalization.map Q (RingHom.id R) ⋯) a- Defined in
- Mathlib.RingTheory.Localization.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Submonoidstatement and proof · cited by 3,086
- AlgEquivstatement · cited by 1,681
- IsLocalizationstatement and proof · cited by 636
- IsLocalization.mapstatement · cited by 99
- RingEquiv.reflstatement · cited by 72
- IsLocalization.algEquivstatement and proof · cited by 45
Cited by5
Results whose statement or proof uses this declaration.
- Module.mem_freeLocus_of_isLocalizationproof · cited by 3
- RatFunc.ofFractionRing_eqproof · cited by 1
- IsLocalization.algEquiv_mk'proof · cited by 1
- RatFunc.toFractionRing_eqproof · cited by 1
- RatFunc.toFractionRingRingEquiv_symm_eqproof · cited by 0