Theorems · Theorem · commutative algebra

not_dvd_differentIdeal_iff

∀ {A : Type u_1} {B : Type u_3} [inst : CommRing A] [inst_1 : CommRing B] [inst_2 : Algebra A B] [inst_3 : IsDomain A]
  [inst_4 : IsDedekindDomain A] [inst_5 : IsDedekindDomain B] [inst_6 : Module.IsTorsionFree A B]
  [inst_7 : Module.Finite A B] [Algebra.IsSeparable (FractionRing A) (FractionRing B)] {P : Ideal B}
  [inst_9 : P.IsPrime], ¬P ∣ differentIdeal A B ↔ Algebra.IsUnramifiedAt A P

A prime does not divide the different ideal iff it is unramified.

Defined in

Mathlib.RingTheory.DedekindDomain.Different

Cited by

1 results in Mathlib

Foundations

Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraIsDomainIsDedekindDomainIsDedekindDomainModule.IsTorsionFreeModule.FiniteAlgebra.IsSeparableIdeal.IsPrime