Theorems · Definition · commutative algebra

Module.FinitePresentation.linearEquivMapExtendScalars

{R : Type u_3} →
  {M : Type u_4} →
    {N : Type u_5} →
      [inst : CommRing R] →
        [inst_1 : AddCommGroup M] →
          [inst_2 : Module R M] →
            [inst_3 : AddCommGroup N] →
              [inst_4 : Module R N] →
                (S : Submonoid R) →
                  [Module.FinitePresentation R M] →
                    LocalizedModule S (M →ₗ[R] N) ≃ₗ[R] LocalizedModule S M →ₗ[Localization S] LocalizedModule S N

Let M be a finitely presented R-module, N an R-module, S : Submonoid R. The linear equivalence between the M →ₗ[R] N localized at S and LocalizedModule S M →ₗ[Localization S] LocalizedModule S N

Defined in

Mathlib.Algebra.Module.FinitePresentation

Cited by

3 results in Mathlib

Foundations

Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleModule.FinitePresentation