Theorems · Theorem · commutative algebra

HomogeneousIdeal.map_le_iff_le_comap

∀ {A : Type u_1} {B : Type u_2} {σ : Type u_4} {τ : Type u_5} {ι : Type u_7} [inst : Semiring A] [inst_1 : Semiring B]
  [inst_2 : SetLike σ A] [inst_3 : SetLike τ B] [inst_4 : AddSubmonoidClass σ A] [inst_5 : AddSubmonoidClass τ B]
  [inst_6 : DecidableEq ι] [inst_7 : AddMonoid ι] {𝒜 : ι → σ} {ℬ : ι → τ} [inst_8 : GradedRing 𝒜]
  [inst_9 : GradedRing ℬ] (f : 𝒜 →+*ᵍ ℬ) {I : HomogeneousIdeal 𝒜} {J : HomogeneousIdeal ℬ},
  HomogeneousIdeal.map f I ≤ J ↔ I ≤ HomogeneousIdeal.comap f J

Defined in

Mathlib.RingTheory.GradedAlgebra.Homogeneous.Maps

Cited by

3 results in Mathlib

Foundations

Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSemiringSetLikeSetLikeAddSubmonoidClassAddSubmonoidClassDecidableEqAddMonoidGradedRingGradedRing