Theorems · Theorem · ring theory

DirectSum.coeAlgHom_of

∀ {ι : Type u_1} {S : Type u_3} {R : Type u_4} [inst : DecidableEq ι] [inst_1 : AddMonoid ι] [inst_2 : CommSemiring S]
  [inst_3 : Semiring R] [inst_4 : Algebra S R] (A : ι → Submodule S R) [inst_5 : SetLike.GradedMonoid A] (i : ι)
  (x : ↥(A i)), (DirectSum.coeAlgHom A) ((DirectSum.of (fun i => ↥(A i)) i) x) = ↑x

Defined in

Mathlib.Algebra.DirectSum.Internal

Cited by

0 results in Mathlib

Foundations

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

Assumes

DecidableEqAddMonoidCommSemiringSemiringAlgebraSetLike.GradedMonoid