Theorems · Theorem · ring theory

DirectSum.decompose_symm_algebraMap

∀ {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] (r : R),
  (DirectSum.decompose 𝒜).symm ((algebraMap R (DirectSum ι fun i => ↥(𝒜 i))) r) = (algebraMap R A) r

Defined in

Mathlib.RingTheory.GradedAlgebra.Basic

Cited by

0 results in Mathlib

Foundations

Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableEqAddMonoidCommSemiringSemiringAlgebraGradedAlgebra