Theorems · Definition · nonassociative algebras

NonUnitalAlgebra.adjoinNonUnitalCommSemiringOfComm

Deprecated since 2026-03-11Use NonUnitalAlgebra.isMulCommutative_adjoin instead.

(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} → (∀ a ∈ s, ∀ b ∈ s, a * b = b * a) → NonUnitalCommSemiring ↥(NonUnitalAlgebra.adjoin R s)

If all elements of s : Set A commute pairwise, then adjoin R s is a non-unital commutative semiring. See note [reducible non-instances].

Defined in

Mathlib.Algebra.Algebra.NonUnitalSubalgebra

Cited by

0 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringNonUnitalSemiringModuleIsScalarTowerSMulCommClass