Theorems · Theorem · nonassociative algebras

Set.smul_mem_center

∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : NonUnitalNonAssocSemiring A] [inst_2 : Module R A]
  [IsScalarTower R A A] [SMulCommClass R A A] (r : R) {a : A}, a ∈ Set.center A → r • a ∈ Set.center A

Defined in

Mathlib.Algebra.Algebra.NonUnitalSubalgebra

Cited by

0 results in Mathlib

Foundations

Depth 8 from the axioms · uses propext

Assumes

CommSemiringNonUnitalNonAssocSemiringModuleIsScalarTowerSMulCommClass