Theorems · Theorem · ring theory

NonUnitalStarAlgHom.map_adjoin_singleton

∀ {F : Type v'} {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 : FunLike F A B] [inst_8 : NonUnitalAlgHomClass F R A B] [inst_9 : StarHomClass F A B] [inst_10 : StarRing R]
  [inst_11 : IsScalarTower R A A] [inst_12 : SMulCommClass R A A] [inst_13 : StarModule R A]
  [inst_14 : IsScalarTower R B B] [inst_15 : SMulCommClass R B B] [inst_16 : StarModule R B] (f : F) (x : A),
  NonUnitalStarSubalgebra.map f (NonUnitalStarAlgebra.adjoin R {x}) = NonUnitalStarAlgebra.adjoin R {f x}

Defined in

Mathlib.Algebra.Star.NonUnitalSubalgebra

Cited by

1 results in Mathlib

Foundations

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

Assumes

CommSemiringNonUnitalSemiringStarRingModuleNonUnitalSemiringStarRingModuleFunLikeNonUnitalAlgHomClassStarHomClassStarRingIsScalarTowerSMulCommClassStarModuleIsScalarTowerSMulCommClassStarModule