Theorems · Theorem · commutative algebra

IsLocalization.AtPrime.equivQuotientMapOfIsMaximal.congr_simp

∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (p p_1 : Ideal R)
  (e_p : p = p_1) [inst_3 : p.IsPrime] (Sₚ : Type u_4) [inst_4 : CommRing Sₚ] [inst_5 : Algebra S Sₚ]
  [inst_6 : IsLocalization (Algebra.algebraMapSubmonoid S p.primeCompl) Sₚ] (P : Ideal S) [hPp : P.LiesOver p]
  [inst_7 : P.IsMaximal],
  IsLocalization.AtPrime.equivQuotientMapOfIsMaximal p Sₚ P =
    IsLocalization.AtPrime.equivQuotientMapOfIsMaximal p_1 Sₚ P

Defined in: Mathlib.RingTheory.Localization.AtPrime.Extension
Cited by: 0 results in Mathlib
Foundations: Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing CommRing Algebra Ideal.IsPrime CommRing Algebra IsLocalization Ideal.LiesOver Ideal.IsMaximal

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites15

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CommRingstatement and proof · cited by 17,173
Algebrastatement and proof · cited by 11,388
RingHomstatement · cited by 10,189
Idealstatement and proof · cited by 4,748
Algebra.algebraMapstatement · cited by 4,706
HasQuotient.Quotientstatement · cited by 2,301
RingEquivstatement · cited by 1,147
Ideal.IsPrimestatement and proof · cited by 827
Ideal.mapstatement · cited by 692
IsLocalizationstatement and proof · cited by 636
Ideal.primeComplstatement and proof · cited by 462
Ideal.IsMaximalstatement and proof · cited by 452

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.