Theorems · Theorem · commutative algebra

IsLocalRing.primesOver_eq

∀ {R : Type u_1} (A : Type u_2) [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : IsLocalRing A] [IsDedekindDomain A]
  [inst_4 : Algebra R A] [FaithfulSMul R A] [Module.Finite R A] {p : Ideal R} [p.IsMaximal],
  p ≠ ⊥ → p.primesOver A = {IsLocalRing.maximalIdeal A}

Defined in

Mathlib.RingTheory.DedekindDomain.Basic

Cited by

1 results in Mathlib

Foundations

Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingIsLocalRingIsDedekindDomainAlgebraFaithfulSMulModule.FiniteIdeal.IsMaximal