Theorems · Theorem · commutative algebra

Ideal.liesOver_iff_dvd_map

∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : CommRing A] [IsDedekindDomain A] [inst_3 : Algebra R A]
  {p : Ideal R} {P : Ideal A}, P ≠ ⊤ → ∀ [p.IsMaximal], P.LiesOver p ↔ P ∣ Ideal.map (algebraMap R A) p

Defined in

Mathlib.RingTheory.DedekindDomain.Ideal.Basic

Cited by

1 results in Mathlib

Foundations

Depth 145 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingIsDedekindDomainAlgebraIdeal.IsMaximal