Theorems · Definition · ring theory

StarAlgEquiv.ofAlgEquiv

{R : Type u_6} →
  {A : Type u_7} →
    {B : Type u_8} →
      [inst : CommSemiring R] →
        [inst_1 : Semiring A] →
          [inst_2 : Semiring B] →
            [inst_3 : Algebra R A] →
              [inst_4 : Algebra R B] →
                [inst_5 : Star A] →
                  [inst_6 : Star B] → (f : A ≃ₐ[R] B) → (∀ (x : A), f (star x) = star (f x)) → A ≃⋆ₐ[R] B

Upgrade an algebra equivalence to a ⋆-algebra equivalence given that it preserves the star operation.

Defined in

Mathlib.Algebra.Star.StarAlgHom

Cited by

4 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringSemiringAlgebraAlgebraStarStar