Theorems · Definition · nonassociative algebras

NonUnitalSubalgebra.prod

{R : Type u} →
  {A : Type v} →
    {B : Type w} →
      [inst : CommSemiring R] →
        [inst_1 : NonUnitalNonAssocSemiring A] →
          [inst_2 : Module R A] →
            NonUnitalSubalgebra R A →
              [inst_3 : NonUnitalNonAssocSemiring B] →
                [inst_4 : Module R B] → NonUnitalSubalgebra R B → NonUnitalSubalgebra R (A × B)

The product of two non-unital subalgebras is a non-unital subalgebra.

Defined in

Mathlib.Algebra.Algebra.NonUnitalSubalgebra

Cited by

8 results in Mathlib

Foundations

Depth 18 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringNonUnitalNonAssocSemiringModuleNonUnitalNonAssocSemiringModule