Theorems · Theorem · commutative algebra

Ideal.quotientEquiv_apply

∀ {R : Type u} [inst : Ring R] {S : Type v} [inst_1 : Ring S] (I : Ideal R) (J : Ideal S) [inst_2 : I.IsTwoSided]
  [inst_3 : J.IsTwoSided] (f : R ≃+* S) (hIJ : J = Ideal.map (↑f) I) (a : R ⧸ I),
  (I.quotientEquiv J f hIJ) a = (↑↑(Ideal.quotientMap J ↑f ⋯)).toFun a

Defined in

Mathlib.RingTheory.Ideal.Quotient.Operations

Cited by

0 results in Mathlib

Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingRingIdeal.IsTwoSidedIdeal.IsTwoSided