Theorems · Definition · ring theory

Subalgebra.pointwiseMulAction

{R : Type u_1} →
  {A : Type u_2} →
    [inst : CommSemiring R] →
      [inst_1 : Semiring A] →
        [inst_2 : Algebra R A] →
          {R' : Type u_3} →
            [inst_3 : Semiring R'] →
              [inst_4 : MulSemiringAction R' A] → [SMulCommClass R' R A] → MulAction R' (Subalgebra R A)

The action on a subalgebra corresponding to applying the action to every element. This is available as an instance in the Pointwise locale.

Defined in

Mathlib.Algebra.Algebra.Subalgebra.Pointwise

Cited by

5 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringAlgebraSemiringMulSemiringActionSMulCommClass