Theorems · Definition · ring theory

AlgEquiv.ofInjective

{R : Type u} →
  {A : Type v} →
    {B : Type w} →
      [inst : CommSemiring R] →
        [inst_1 : Semiring A] →
          [inst_2 : Semiring B] →
            [inst_3 : Algebra R A] → [inst_4 : Algebra R B] → (f : A →ₐ[R] B) → Function.Injective ⇑f → A ≃ₐ[R] ↥f.range

Restrict an injective algebra homomorphism to an algebra isomorphism

Defined in

Mathlib.Algebra.Algebra.Subalgebra.Basic

Cited by

16 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringSemiringAlgebraAlgebra