Theorems · Theorem · nonassociative algebras

NonUnitalSubalgebra.prod_inf_prod

∀ {R : Type u} {A : Type v} {B : Type w} [inst : CommSemiring R] [inst_1 : NonUnitalNonAssocSemiring A]
  [inst_2 : Module R A] [inst_3 : NonUnitalNonAssocSemiring B] [inst_4 : Module R B] [inst_5 : IsScalarTower R A A]
  [inst_6 : SMulCommClass R A A] [inst_7 : IsScalarTower R B B] [inst_8 : SMulCommClass R B B]
  {S T : NonUnitalSubalgebra R A} {S₁ T₁ : NonUnitalSubalgebra R B}, S.prod S₁ ⊓ T.prod T₁ = (S ⊓ T).prod (S₁ ⊓ T₁)

Defined in

Mathlib.Algebra.Algebra.NonUnitalSubalgebra

Cited by

0 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringNonUnitalNonAssocSemiringModuleNonUnitalNonAssocSemiringModuleIsScalarTowerSMulCommClassIsScalarTowerSMulCommClass