Theorems · Theorem · commutative algebra

Ideal.map_comap_of_equiv

∀ {R : Type u} {S : Type v} [inst : Semiring R] [inst_1 : Semiring S] {I : Ideal R} (f : R ≃+* S),
  Ideal.map (↑f) I = Ideal.comap f.symm I

If f : R ≃+* S is a ring isomorphism and I : Ideal R, then map f I = comap f.symm I.

Defined in

Mathlib.RingTheory.Ideal.Maps

Cited by

6 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Quot.sound

Assumes

SemiringSemiring