Theorems · Theorem · nonassociative algebras

NonUnitalAlgebra.isMulCommutative_adjoin

∀ (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] {s : Set A},
  (∀ x ∈ s, ∀ y ∈ s, x * y = y * x) → IsMulCommutative ↥(NonUnitalAlgebra.adjoin R s)

If all elements of s : Set A commute pairwise, then adjoin R s is commutative.

Defined in

Mathlib.Algebra.Algebra.NonUnitalSubalgebra

Cited by

0 results in Mathlib

Foundations

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

Assumes

CommSemiringNonUnitalSemiringModuleIsScalarTowerSMulCommClass