Theorems · Definition · ring theory

StarAlgEquiv.ofInjective

{R : Type u_2} →
  {A : Type u_3} →
    {B : Type u_4} →
      [inst : CommSemiring R] →
        [inst_1 : StarRing R] →
          [inst_2 : Semiring A] →
            [inst_3 : Algebra R A] →
              [inst_4 : StarRing A] →
                [inst_5 : Semiring B] →
                  [inst_6 : Algebra R B] →
                    [inst_7 : StarRing B] →
                      [inst_8 : StarModule R B] → (f : A →⋆ₐ[R] B) → Function.Injective ⇑f → A ≃⋆ₐ[R] ↥f.range

The StarAlgEquiv onto the range corresponding to an injective StarAlgHom.

Defined in

Mathlib.Algebra.Star.Subalgebra

Cited by

2 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringStarRingSemiringAlgebraStarRingSemiringAlgebraStarRingStarModule