Theorems · Definition · commutative algebra

IsLocalizedModule.Away

{R : Type u_1} →
  {M : Type u_2} →
    {M' : Type u_3} →
      [inst : CommSemiring R] →
        R →
          [inst_1 : AddCommMonoid M] →
            [inst_2 : Module R M] → [inst_3 : AddCommMonoid M'] → [inst_4 : Module R M'] → (M →ₗ[R] M') → Prop

Given x : R and f : M →ₗ[R] M', IsLocalizedModule.Away x f states that M' is isomorphic to the localization of M at the submonoid generated by x.

Defined in

Mathlib.Algebra.Module.LocalizedModule.Basic

Cited by

27 results in Mathlib

Foundations

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

Assumes

CommSemiringAddCommMonoidModuleAddCommMonoidModule