On graphs and valuations

Ido Efrat, Andrei S. Rapinchuk, Yoav Segev

Research output: Contribution to journalArticlepeer-review


In the last two decades new techniques emerged to construct valuations on an infinite division ring D, given a normal subgroup N⊆D× of finite index. These techniques were based on the commuting graph of D×/N in the case where D is non-commutative, and on the Milnor K-graph on D×/N, in the case where D is commutative. In this paper we unify these two approaches and consider V-graphs on D×/N and how they lead to valuations. We furthermore generalize previous results to situations of finitely many valuations.

Original languageEnglish
Pages (from-to)395-432
Number of pages38
JournalManuscripta Mathematica
Issue number3-4
StatePublished - 1 Mar 2015


  • 12J10
  • 16K20
  • 19D45
  • Primary 16W60
  • Secondary 05C25

ASJC Scopus subject areas

  • General Mathematics


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