Theorems · Definition · ring theory

MulSemiringAction.toAlgEquiv

{G : Type u_2} →
  (R : Type u_3) →
    (A : Type u_4) →
      [inst : CommSemiring R] →
        [inst_1 : Semiring A] →
          [inst_2 : Algebra R A] →
            [inst_3 : Group G] → [inst_4 : MulSemiringAction G A] → [SMulCommClass G R A] → G → A ≃ₐ[R] A

Each element of the group defines an algebra equivalence. This is a stronger version of MulSemiringAction.toRingEquiv and DistribMulAction.toLinearEquiv.

Defined in

Mathlib.Algebra.Algebra.Equiv

Cited by

11 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringAlgebraGroupMulSemiringActionSMulCommClass