Theorems · Theorem · ring theory

DirectSum.decompose_mul

∀ {ι : Type u_1} {A : Type u_3} {σ : Type u_4} [inst : DecidableEq ι] [inst_1 : AddMonoid ι] [inst_2 : Semiring A]
  [inst_3 : SetLike σ A] [inst_4 : AddSubmonoidClass σ A] (𝒜 : ι → σ) [inst_5 : GradedRing 𝒜] (x y : A),
  (DirectSum.decompose 𝒜) (x * y) = (DirectSum.decompose 𝒜) x * (DirectSum.decompose 𝒜) y

Defined in

Mathlib.RingTheory.GradedAlgebra.Basic

Cited by

12 results in Mathlib

Foundations

Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableEqAddMonoidSemiringSetLikeAddSubmonoidClassGradedRing