Theorems · Theorem · commutative algebra

IsDedekindDomain.HeightOneSpectrum.adicCompletion.ext

∀ {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)
  {x y : IsDedekindDomain.HeightOneSpectrum.adicCompletion K v}, x.toCompletion = y.toCompletion → x = y

Defined in

Mathlib.RingTheory.DedekindDomain.AdicValuation

Cited by

6 results in Mathlib

Foundations

Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsDedekindDomainFieldAlgebraIsFractionRing