Theorems · Theorem · nonassociative algebras

NonUnitalAlgHom.range_comp

∀ {R : Type u} {A : Type v} {B : Type w} {C : 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 : NonUnitalNonAssocSemiring C] [inst_6 : Module R C] (f : A →ₙₐ[R] B) (g : B →ₙₐ[R] C),
  NonUnitalAlgHom.range (g.comp f) = NonUnitalSubalgebra.map g (NonUnitalAlgHom.range f)

Defined in

Mathlib.Algebra.Algebra.NonUnitalSubalgebra

Cited by

0 results in Mathlib

Foundations

Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringNonUnitalNonAssocSemiringModuleNonUnitalNonAssocSemiringModuleNonUnitalNonAssocSemiringModule