Theorems · Theorem · commutative algebra

Ideal.mul_homogeneous_element_mem_of_mem

∀ {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] [inst_5 : GradedRing 𝒜]
  {I : Ideal A} (r x : A), SetLike.IsHomogeneousElem 𝒜 x → x ∈ I → ∀ (j : ι), (GradedRing.proj 𝒜 j) (r * x) ∈ I

Defined in

Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal

Cited by

1 results in Mathlib

Foundations

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

Assumes

SemiringSetLikeAddSubmonoidClassDecidableEqAddMonoidGradedRing