Theorems · Theorem · commutative algebra

not_dvd_differentIdeal_of_intTrace_not_mem

∀ (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 A} (P Q : Ideal B),
  P * Q = Ideal.map (algebraMap A B) p → ∀ x ∈ Q, (Algebra.intTrace A B) x ∉ p → ¬P ∣ differentIdeal A B

Defined in

Mathlib.RingTheory.DedekindDomain.Different

Cited by

1 results in Mathlib

Foundations

Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraIsDomainIsDedekindDomainIsDedekindDomainModule.IsTorsionFreeModule.FiniteAlgebra.IsSeparable