Theorems · Theorem · nonassociative algebras

NonUnitalAlgHom.map_adjoin

∀ {F : Type u_1} (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 : FunLike F A B]
  [inst_6 : NonUnitalAlgHomClass F R A 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] (f : F) (s : Set A),
  NonUnitalSubalgebra.map f (NonUnitalAlgebra.adjoin R s) = NonUnitalAlgebra.adjoin R (⇑f '' s)

Defined in

Mathlib.Algebra.Algebra.NonUnitalSubalgebra

Cited by

1 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringNonUnitalNonAssocSemiringModuleNonUnitalNonAssocSemiringModuleFunLikeNonUnitalAlgHomClassIsScalarTowerSMulCommClassIsScalarTowerSMulCommClass