Theorems · Theorem · ring theory

AlgHom.range_comp

∀ {R : Type u} {A : Type v} {B : Type w} {C : Type w'} [inst : CommSemiring R] [inst_1 : Semiring A]
  [inst_2 : Algebra R A] [inst_3 : Semiring B] [inst_4 : Algebra R B] [inst_5 : Semiring C] [inst_6 : Algebra R C]
  (f : A →ₐ[R] B) (g : B →ₐ[R] C), (g.comp f).range = Subalgebra.map g f.range

Defined in

Mathlib.Algebra.Algebra.Subalgebra.Basic

Cited by

5 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringAlgebraSemiringAlgebraSemiringAlgebra