Theorems · Definition · ring theory

StarAlgEquiv.restrictScalars

(R : Type u_1) →
  {S : Type u_2} →
    {A : Type u_3} →
      {B : Type u_4} →
        [inst : CommSemiring R] →
          [inst_1 : CommSemiring S] →
            [inst_2 : NonUnitalNonAssocSemiring A] →
              [inst_3 : NonUnitalNonAssocSemiring B] →
                [inst_4 : MulAction R S] →
                  [inst_5 : Module S A] →
                    [inst_6 : Module S B] →
                      [inst_7 : Module R A] →
                        [inst_8 : Module R B] →
                          [IsScalarTower R S A] →
                            [IsScalarTower R S B] → [inst_11 : Star A] → [inst_12 : Star B] → (A ≃⋆ₐ[S] B) → A ≃⋆ₐ[R] B

Restrict the scalar ring of a star algebra equivalence.

Defined in

Mathlib.Algebra.Star.Subalgebra

Cited by

5 results in Mathlib

Foundations

Depth 26 from the axioms · uses Quot.sound

Assumes

CommSemiringCommSemiringNonUnitalNonAssocSemiringNonUnitalNonAssocSemiringMulActionModuleModuleModuleModuleIsScalarTowerIsScalarTowerStarStar