Theorems · Definition · ring theory

AlgEquiv.subalgebraMap

{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] → (e : A ≃ₐ[R] B) → (S : Subalgebra R A) → ↥S ≃ₐ[R] ↥(Subalgebra.map (↑e) S)

Given an equivalence e : A ≃ₐ[R] B of R-algebras and a subalgebra S of A, subalgebraMap is the induced equivalence between S and S.map e

Defined in

Mathlib.Algebra.Algebra.Subalgebra.Basic

Cited by

2 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringSemiringAlgebraAlgebra