Theorems · Definition · commutative algebra

Submodule.localizedEquiv

{R : Type u_1} →
  {M : Type u_3} →
    [inst : CommSemiring R] →
      [inst_1 : AddCommMonoid M] →
        [inst_2 : Module R M] →
          (p : Submonoid R) →
            (M' : Submodule R M) → ↥(Submodule.localized p M') ≃ₗ[Localization p] LocalizedModule p ↥M'

The canonical isomorphism between the localization of a submodule and its realization as a submodule in the localized module.

Defined in

Mathlib.Algebra.Module.LocalizedModule.Submodule

Cited by

0 results in Mathlib

Foundations

Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModule