Theorems · Theorem · ring theory

DirectSum.coe_decompose_mul_add_of_right_mem

∀ {ι : Type u_1} {A : Type u_3} {σ : Type u_4} [inst : DecidableEq ι] [inst_1 : Semiring A] [inst_2 : SetLike σ A]
  [inst_3 : AddSubmonoidClass σ A] (𝒜 : ι → σ) {i j : ι} [inst_4 : AddRightCancelMonoid ι] [inst_5 : GradedRing 𝒜]
  {a b : A}, b ∈ 𝒜 j → ↑(((DirectSum.decompose 𝒜) (a * b)) (i + j)) = ↑(((DirectSum.decompose 𝒜) a) i) * b

Defined in

Mathlib.RingTheory.GradedAlgebra.Basic

Cited by

2 results in Mathlib

Foundations

Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableEqSemiringSetLikeAddSubmonoidClassAddRightCancelMonoidGradedRing