Theorems · Definition · commutative algebra

HomogeneousIdeal

{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] → Type u_3

For any Semiring A, we collect the homogeneous ideals of A into a type.

Defined in

Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal

Cited by

115 results in Mathlib

Foundations

Depth 14 from the axioms, rests on 163 definitions · uses no axioms

Assumes

SemiringSetLikeAddSubmonoidClassDecidableEqAddMonoidGradedRing