Theorems · Theorem · commutative algebra

Ideal.quotientEquivAlg.congr_simp

∀ {R₁ : Type u_1} {A : Type u_3} {B : Type u_4} [inst : CommSemiring R₁] [inst_1 : Ring A] [inst_2 : Algebra R₁ A]
  [inst_3 : Ring B] [inst_4 : Algebra R₁ B] (I : Ideal A) (J : Ideal B) [inst_5 : I.IsTwoSided] [inst_6 : J.IsTwoSided]
  (f f_1 : A ≃ₐ[R₁] B) (e_f : f = f_1) (hIJ : J = Ideal.map (↑f) I),
  I.quotientEquivAlg J f hIJ = I.quotientEquivAlg J f_1 ⋯

Defined in

Mathlib.RingTheory.Etale.StandardEtale

Cited by

0 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringRingAlgebraRingAlgebraIdeal.IsTwoSidedIdeal.IsTwoSided