Theorems · Definition · commutative algebra

Ideal.IsHomogeneous

{ι : Type u_1} →
  {σ : Type u_2} →
    {A : Type u_3} →
      [inst : Semiring A] →
        [inst_1 : SetLike σ A] →
          [inst_2 : AddSubmonoidClass σ A] →
            (𝒜 : ι → σ) → [inst_3 : DecidableEq ι] → [inst_4 : AddMonoid ι] → [GradedRing 𝒜] → Ideal A → Prop

An I : Ideal A is homogeneous if for every r ∈ I, all homogeneous components of r are in I.

Defined in

Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal

Cited by

30 results in Mathlib

Foundations

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

Assumes

SemiringSetLikeAddSubmonoidClassDecidableEqAddMonoidGradedRing