Theorems · Theorem · commutative algebra

IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.mem_units_iff_valued_eq_one

∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDedekindDomain R] {K : Type u_2} [inst_2 : Field K]
  [inst_3 : Algebra R K] [inst_4 : IsFractionRing R K] {v : IsDedekindDomain.HeightOneSpectrum R}
  {a : (IsDedekindDomain.HeightOneSpectrum.adicCompletion K v)ˣ},
  a ∈ (IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers K v).units ↔ Valued.v ↑a = 1

Defined in

Mathlib.RingTheory.DedekindDomain.AdicValuation

Cited by

1 results in Mathlib

Foundations

Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsDedekindDomainFieldAlgebraIsFractionRing