Theorems · Theorem · number theory

IsDedekindDomain.FiniteAdeleRing.isUnit_iff

∀ {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] {a : IsDedekindDomain.FiniteAdeleRing R K},
  IsUnit a ↔
    (∀ (v : IsDedekindDomain.HeightOneSpectrum R), a v ≠ 0) ∧
      ∀ᶠ (v : IsDedekindDomain.HeightOneSpectrum R) in Filter.cofinite, Valued.v (a v) = 1

Defined in

Mathlib.RingTheory.DedekindDomain.FiniteAdeleRing

Cited by

1 results in Mathlib

Foundations

Depth 192 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsDedekindDomainFieldAlgebraIsFractionRing