Theorems · Theorem · ring theory

NonUnitalStarSubalgebra.center_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]
  [inst_7 : IsScalarTower R A A] [inst_8 : SMulCommClass R A A] [inst_9 : IsScalarTower R B B]
  [inst_10 : SMulCommClass R B B],
  NonUnitalStarSubalgebra.center R (A × B) =
    (NonUnitalStarSubalgebra.center R A).prod (NonUnitalStarSubalgebra.center R B)

Defined in

Mathlib.Algebra.Star.NonUnitalSubalgebra

Cited by

0 results in Mathlib

Foundations

Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringNonUnitalSemiringStarRingModuleNonUnitalSemiringStarRingModuleIsScalarTowerSMulCommClassIsScalarTowerSMulCommClass