Theorems · Theorem · commutative algebra

IsDedekindDomain.HeightOneSpectrum.adicAbv_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) {b : NNReal}
  (hb : 1 < b) (r : R), (v.adicAbv hb) ((algebraMap R K) r) = (v.intAdicAbv hb) r

The v-adic absolute value on K extends the v-adic absolute value on R.

Defined in

Mathlib.RingTheory.DedekindDomain.AdicValuation

Cited by

3 results in Mathlib

Foundations

Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsDedekindDomainFieldAlgebraIsFractionRing