Theorems · Definition · commutative algebra

IsLocalization.orderIsoOfPrime

{R : Type u_1} →
  [inst : CommSemiring R] →
    (M : Submonoid R) →
      (S : Type u_2) →
        [inst_1 : CommSemiring S] →
          [inst_2 : Algebra R S] → [IsLocalization M S] → { p // p.IsPrime } ≃o { p // p.IsPrime ∧ Disjoint ↑M ↑p }

If R is a ring, then prime ideals in the localization at M correspond to prime ideals in the original ring R that are disjoint from M

Defined in

Mathlib.RingTheory.Localization.Ideal

Cited by

4 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommSemiringAlgebraIsLocalization