Theorems · Definition · ring theory

mulSemiringActionOfSmulDistribClass

(R : Type u_1) →
  (A : Type u_2) →
    [inst : CommSemiring R] →
      [inst_1 : Semiring A] →
        [inst_2 : Algebra R A] →
          [FaithfulSMul R A] →
            (G : Type u_3) →
              [inst_4 : Monoid G] →
                [inst_5 : MulSemiringAction G A] →
                  [inst_6 : SMul G R] → [SMulDistribClass G R A] → MulSemiringAction G R

If R embeds faithfully into A and G satisfies SMulDistribClass G R A, then the SMul of G on R extends to a MulSemiringAction.

Defined in

Mathlib.Algebra.Algebra.Basic

Cited by

1 results in Mathlib

Foundations

Depth 23 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringAlgebraFaithfulSMulMonoidMulSemiringActionSMulSMulDistribClass