Theorems · Theorem · nonassociative algebras

NonUnitalSubalgebra.map_toSubmodule

∀ {F : Type v'} {R : Type u} {A : Type v} {B : Type w} [inst : CommSemiring R] [inst_1 : NonUnitalNonAssocSemiring A]
  [inst_2 : NonUnitalNonAssocSemiring B] [inst_3 : Module R A] [inst_4 : Module R B] [inst_5 : FunLike F A B]
  [inst_6 : NonUnitalAlgHomClass F R A B] {S : NonUnitalSubalgebra R A} {f : F},
  (NonUnitalSubalgebra.map f S).toSubmodule = Submodule.map (LinearMapClass.linearMap f) S.toSubmodule

Defined in

Mathlib.Algebra.Algebra.NonUnitalSubalgebra

Cited by

0 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringNonUnitalNonAssocSemiringNonUnitalNonAssocSemiringModuleModuleFunLikeNonUnitalAlgHomClass