Theorems · Theorem · ring theory

algebra_compatible_smul

∀ {R : Type u_1} [inst : CommSemiring R] (A : Type u_2) [inst_1 : Semiring A] [inst_2 : Algebra R A] {M : Type u_3}
  [inst_3 : AddCommMonoid M] [inst_4 : Module A M] [inst_5 : Module R M] [IsScalarTower R A M] (r : R) (m : M),
  r • m = (algebraMap R A) r • m

Defined in

Mathlib.Algebra.Algebra.Basic

Cited by

7 results in Mathlib

Foundations

Depth 18 from the axioms · uses no axioms

Assumes

CommSemiringSemiringAlgebraAddCommMonoidModuleModuleIsScalarTower