Theorems · Theorem · commutative algebra

IsDedekindDomain.HeightOneSpectrum.valuation_of_algebraMap

∀ {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) (r : R),
  (IsDedekindDomain.HeightOneSpectrum.valuation K v) ↑r = v.intValuation r

The v-adic valuation on K extends the v-adic valuation on R.

Defined in

Mathlib.RingTheory.DedekindDomain.AdicValuation

Cited by

23 results in Mathlib

Foundations

Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsDedekindDomainFieldAlgebraIsFractionRing