Theorems · Theorem · commutative algebra

DirectSum.SetLike.IsHomogeneous.mem_iff

∀ {ι : Type u_1} {σ : Type u_2} {A : Type u_3} [inst : AddMonoid ι] [inst_1 : Semiring A] [inst_2 : SetLike σ A]
  [inst_3 : AddSubmonoidClass σ A] (𝒜 : ι → σ) [inst_4 : DecidableEq ι] [inst_5 : GradedRing 𝒜] {R : Subsemiring A},
  DirectSum.SetLike.IsHomogeneous 𝒜 R → ∀ {a : A}, a ∈ R ↔ ∀ (i : ι), ↑(((DirectSum.decompose 𝒜) a) i) ∈ R

Defined in

Mathlib.RingTheory.GradedAlgebra.Homogeneous.Subsemiring

Cited by

0 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddMonoidSemiringSetLikeAddSubmonoidClassDecidableEqGradedRing