Theorems · Theorem · commutative algebra

IsDedekindDomain.HeightOneSpectrum.algebraMap_adicCompletion

∀ (R : Type u_1) [inst : CommRing R] [inst_1 : IsDedekindDomain R] (K : Type u_2) {S : Type u_3} [inst_2 : Field K]
  [inst_3 : CommSemiring S] [inst_4 : Algebra R K] [inst_5 : IsFractionRing R K]
  (v : IsDedekindDomain.HeightOneSpectrum R) [inst_6 : Algebra S K],
  ⇑(algebraMap S (IsDedekindDomain.HeightOneSpectrum.adicCompletion K v)) =
    (fun x => { toCompletion := ↑((WithVal.equiv (IsDedekindDomain.HeightOneSpectrum.valuation K v)).symm x) }) ∘
      ⇑(algebraMap S K)

Defined in

Mathlib.RingTheory.DedekindDomain.AdicValuation

Cited by

1 results in Mathlib

Foundations

Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsDedekindDomainFieldCommSemiringAlgebraIsFractionRingAlgebra