Theorems · Definition · ring theory

NonUnitalStarSubalgebra.prod

{R : Type u} →
  {A : Type v} →
    {B : Type w} →
      [inst : CommSemiring R] →
        [inst_1 : NonUnitalSemiring A] →
          [inst_2 : StarRing A] →
            [inst_3 : Module R A] →
              [inst_4 : NonUnitalSemiring B] →
                [inst_5 : StarRing B] →
                  [inst_6 : Module R B] →
                    NonUnitalStarSubalgebra R A → NonUnitalStarSubalgebra R B → NonUnitalStarSubalgebra R (A × B)

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

Defined in

Mathlib.Algebra.Star.NonUnitalSubalgebra

Cited by

7 results in Mathlib

Foundations

Depth 20 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringNonUnitalSemiringStarRingModuleNonUnitalSemiringStarRingModule