Theorems · Theorem · commutative algebra

Ideal.map_le_comap_of_inverse

∀ {R : Type u} {S : Type v} {F : Type u_1} [inst : Semiring R] [inst_1 : Semiring S] [inst_2 : FunLike F R S] (f : F)
  {G : Type u_2} [inst_3 : FunLike G S R] [inst_4 : RingHomClass G S R] (g : G) (I : Ideal R),
  Function.LeftInverse ⇑g ⇑f → Ideal.map f I ≤ Ideal.comap g I

The Ideal version of Set.image_subset_preimage_of_inverse.

Defined in

Mathlib.RingTheory.Ideal.Maps

Cited by

1 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Quot.sound

Assumes

SemiringSemiringFunLikeFunLikeRingHomClass