Theorems · Definition · ring theory

DirectSum.coeRingHom

{ι : Type u_1} →
  {σ : Type u_2} →
    {R : Type u_4} →
      [inst : DecidableEq ι] →
        [inst_1 : Semiring R] →
          [inst_2 : SetLike σ R] →
            [inst_3 : AddSubmonoidClass σ R] →
              (A : ι → σ) →
                [inst_4 : AddMonoid ι] → [inst_5 : SetLike.GradedMonoid A] → (DirectSum ι fun i => ↥(A i)) →+* R

The canonical ring isomorphism between ⨁ i, A i and R

Defined in

Mathlib.Algebra.DirectSum.Internal

Cited by

1 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableEqSemiringSetLikeAddSubmonoidClassAddMonoidSetLike.GradedMonoid