Theorems · Theorem · number theory

Set.integer_eq

∀ {R : Type u} [inst : CommRing R] [inst_1 : IsDedekindDomain R] (S : Set (IsDedekindDomain.HeightOneSpectrum R))
  (K : Type v) [inst_2 : Field K] [inst_3 : Algebra R K] [inst_4 : IsFractionRing R K],
  (S.integer K).toSubring =
    ⨅ v, ⨅ (_ : v ∉ S), (IsDedekindDomain.HeightOneSpectrum.valuation K v).valuationSubring.toSubring

Defined in

Mathlib.RingTheory.DedekindDomain.SInteger

Cited by

0 results in Mathlib

Foundations

Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsDedekindDomainFieldAlgebraIsFractionRing