Theorems · Theorem · commutative algebra

HomogeneousIdeal.mem_irrelevant_of_mem

∀ {ι : Type u_1} {σ : Type u_2} {A : Type u_3} [inst : Semiring A] [inst_1 : DecidableEq ι] [inst_2 : AddCommMonoid ι]
  [inst_3 : PartialOrder ι] [inst_4 : CanonicallyOrderedAdd ι] [inst_5 : SetLike σ A] [inst_6 : AddSubmonoidClass σ A]
  (𝒜 : ι → σ) [inst_7 : GradedRing 𝒜] {x : A} {i : ι}, 0 < i → x ∈ 𝒜 i → x ∈ HomogeneousIdeal.irrelevant 𝒜

Defined in

Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal

Cited by

2 results in Mathlib

Foundations

Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringDecidableEqAddCommMonoidPartialOrderCanonicallyOrderedAddSetLikeAddSubmonoidClassGradedRing