Theorems · Definition · commutative algebra

DistribMulAction.toLinearEquiv

(R : Type u_1) →
  {S : Type u_4} →
    (M : Type u_5) →
      [inst : Semiring R] →
        [inst_1 : AddCommMonoid M] →
          [inst_2 : Module R M] →
            [inst_3 : Group S] → [inst_4 : DistribMulAction S M] → [SMulCommClass S R M] → S → M ≃ₗ[R] M

Each element of the group defines a linear equivalence. This is a stronger version of DistribMulAction.toAddEquiv.

Defined in

Mathlib.Algebra.Module.Equiv.Basic

Cited by

8 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleGroupDistribMulActionSMulCommClass