Theorems · Definition · commutative algebra

LinearEquiv.toLinearMap

{R : Type u_14} →
  {S : Type u_15} →
    [inst : Semiring R] →
      [inst_1 : Semiring S] →
        {σ : R →+* S} →
          {σ' : S →+* R} →
            [inst_2 : RingHomInvPair σ σ'] →
              [inst_3 : RingHomInvPair σ' σ] →
                {M : Type u_16} →
                  {M₂ : Type u_17} →
                    [inst_4 : AddCommMonoid M] →
                      [inst_5 : AddCommMonoid M₂] →
                        [inst_6 : Module R M] → [inst_7 : Module S M₂] → (M ≃ₛₗ[σ] M₂) → M →ₛₗ[σ] M₂

The linear map underlying a linear equivalence.

Defined in

Mathlib.Algebra.Module.Equiv.Defs

Cited by

1,171 results in Mathlib

Foundations

Depth 13 from the axioms, rests on 85 definitions · uses no axioms

Assumes

SemiringSemiringRingHomInvPairRingHomInvPairAddCommMonoidAddCommMonoidModuleModule