Theorems · Theorem · commutative algebra

FractionalIdeal.count_maximal_coprime

∀ {R : Type u_1} [inst : CommRing R] (K : Type u_2) [inst_1 : Field K] [inst_2 : Algebra R K]
  [inst_3 : IsFractionRing R K] [inst_4 : IsDedekindDomain R] (v : IsDedekindDomain.HeightOneSpectrum R)
  {w : IsDedekindDomain.HeightOneSpectrum R}, w ≠ v → FractionalIdeal.count K v ↑w.asIdeal = 0

If v ≠ w are two maximal ideals of R, then val_v(w) = 0.

Defined in

Mathlib.RingTheory.DedekindDomain.Factorization

Cited by

2 results in Mathlib

Foundations

Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingFieldAlgebraIsFractionRingIsDedekindDomain