Theorems · Theorem · ring theory
DirectSum.coe_decompose_mul_of_right_mem_zero
∀ {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 : ι} [inst_4 : AddMonoid ι] [inst_5 : GradedRing 𝒜] {a b : A},
b ∈ 𝒜 0 → ↑(((DirectSum.decompose 𝒜) (a * b)) i) = ↑(((DirectSum.decompose 𝒜) a) i) * b- Defined in
- Mathlib.RingTheory.GradedAlgebra.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Equivstatement · cited by 8,337
- AddMonoidstatement and proof · cited by 2,864
- SetLikestatement and proof · cited by 1,084
- DFinsuppstatement · cited by 694
- DirectSumstatement and proof · cited by 446
- GradedRingstatement and proof · cited by 424
- AddSubmonoidClassstatement and proof · cited by 346
- DirectSum.decomposestatement and proof · cited by 93
- DirectSum.decompose_coeproof · cited by 17
- DirectSum.decompose_mulproof · cited by 12
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