Theorems · Theorem · ring theory

NonUnitalStarAlgebra.map_iInf

∀ {F : Type v'} {R : Type u} {A : Type v} {B : Type w} [inst : CommSemiring R] [inst_1 : StarRing R]
  [inst_2 : NonUnitalSemiring A] [inst_3 : StarRing A] [inst_4 : Module R A] [inst_5 : NonUnitalSemiring B]
  [inst_6 : StarRing B] [inst_7 : Module R B] [inst_8 : FunLike F A B] [inst_9 : NonUnitalAlgHomClass F R A B]
  [inst_10 : StarHomClass F A B] [inst_11 : IsScalarTower R A A] [inst_12 : SMulCommClass R A A]
  [inst_13 : StarModule R A] {ι : Sort u_1} [Nonempty ι] [inst_15 : IsScalarTower R B B] [inst_16 : SMulCommClass R B B]
  [inst_17 : StarModule R B] (f : F),
  Function.Injective ⇑f →
    ∀ (S : ι → NonUnitalStarSubalgebra R A),
      NonUnitalStarSubalgebra.map f (⨅ i, S i) = ⨅ i, NonUnitalStarSubalgebra.map f (S i)

Defined in

Mathlib.Algebra.Star.NonUnitalSubalgebra

Cited by

0 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringStarRingNonUnitalSemiringStarRingModuleNonUnitalSemiringStarRingModuleFunLikeNonUnitalAlgHomClassStarHomClassIsScalarTowerSMulCommClassStarModuleNonemptyIsScalarTowerSMulCommClassStarModule