Theorems · Theorem · ring theory

NonUnitalStarSubalgebra.prod_inf_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 : StarRing R]
  [inst_8 : IsScalarTower R A A] [inst_9 : SMulCommClass R A A] [inst_10 : StarModule R A]
  [inst_11 : IsScalarTower R B B] [inst_12 : SMulCommClass R B B] [inst_13 : StarModule R B]
  {S T : NonUnitalStarSubalgebra R A} {S₁ T₁ : NonUnitalStarSubalgebra R B},
  S.prod S₁ ⊓ T.prod T₁ = (S ⊓ T).prod (S₁ ⊓ T₁)

Defined in

Mathlib.Algebra.Star.NonUnitalSubalgebra

Cited by

0 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringNonUnitalSemiringStarRingModuleNonUnitalSemiringStarRingModuleStarRingIsScalarTowerSMulCommClassStarModuleIsScalarTowerSMulCommClassStarModule