Theorems · Theorem · nonassociative algebras

NonUnitalAlgebra.commute_of_mem_adjoin_of_forall_mem_commute

∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : NonUnitalSemiring A] [inst_2 : Module R A]
  [inst_3 : IsScalarTower R A A] [inst_4 : SMulCommClass R A A] {a b : A} {s : Set A},
  b ∈ NonUnitalAlgebra.adjoin R s → (∀ b ∈ s, Commute a b) → Commute a b

Defined in

Mathlib.Algebra.Algebra.NonUnitalSubalgebra

Cited by

2 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringNonUnitalSemiringModuleIsScalarTowerSMulCommClass