Theorems · Definition · ring theory

Subalgebra.equivMapOfInjective

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

A subalgebra is isomorphic to its image under an injective AlgHom

Defined in

Mathlib.Algebra.Algebra.Subalgebra.Basic

Cited by

2 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringAlgebraSemiringAlgebra