Theorems · Theorem · commutative algebra
Localization.localRingEquiv_symm_apply
∀ {R : Type u_1} [inst : CommSemiring R] {P : Type u_3} [inst_1 : CommSemiring P] (I : Ideal R) [hI : I.IsPrime]
(J : Ideal P) [inst_2 : J.IsPrime] (f : R ≃+* P) (hIJ : I = Ideal.comap f J) (a : Localization.AtPrime J),
(Localization.localRingEquiv I J f hIJ).symm a = (Localization.localRingHom J I ↑f.symm ⋯) a- Cited by
- 0 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
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
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Idealstatement and proof · cited by 4,748
- RingEquivstatement and proof · cited by 1,147
- Ideal.IsPrimestatement and proof · cited by 827
- RingHomClass.toRingHomstatement · cited by 746
- RingEquiv.symmstatement and proof · cited by 567
- Ideal.primeComplstatement · cited by 462
- Ideal.comapstatement and proof · cited by 443
- Localization.AtPrimestatement and proof · cited by 299
- Localization.localRingHomstatement · cited by 54
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