Theorems · Theorem · ring theory

GradedAlgebra.proj_recompose

∀ {ι : Type u_1} {R : Type u_2} {A : Type u_3} [inst : DecidableEq ι] [inst_1 : AddMonoid ι] [inst_2 : CommSemiring R]
  [inst_3 : Semiring A] [inst_4 : Algebra R A] (𝒜 : ι → Submodule R A) [inst_5 : GradedAlgebra 𝒜]
  (a : DirectSum ι fun i => ↥(𝒜 i)) (i : ι),
  (GradedAlgebra.proj 𝒜 i) ((DirectSum.decompose 𝒜).symm a) =
    (DirectSum.decompose 𝒜).symm ((DirectSum.of (fun i => ↥(𝒜 i)) i) (a i))

Defined in

Mathlib.RingTheory.GradedAlgebra.Basic

Cited by

0 results in Mathlib

Foundations

Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableEqAddMonoidCommSemiringSemiringAlgebraGradedAlgebra