Theorems · Definition · commutative algebra

IsLocalizedModule.AtPrime

{R : Type u_1} →
  {M : Type u_2} →
    {M' : Type u_3} →
      [inst : CommSemiring R] →
        (P : Ideal R) →
          [P.IsPrime] →
            [inst_2 : AddCommMonoid M] →
              [inst_3 : AddCommMonoid M'] → [inst_4 : Module R M] → [inst_5 : Module R M'] → (M →ₗ[R] M') → Prop

Given a prime ideal P and f : M →ₗ[R] M', IsLocalizedModule.AtPrime P f states that M' is isomorphic to the localization of M at the complement of P.

Defined in

Mathlib.Algebra.Module.LocalizedModule.AtPrime

Cited by

11 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringIdeal.IsPrimeAddCommMonoidAddCommMonoidModuleModule