Abstract
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 language | English |
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Pages (from-to) | 395-432 |
Number of pages | 38 |
Journal | Manuscripta Mathematica |
Volume | 146 |
Issue number | 3-4 |
DOIs | |
State | Published - 1 Mar 2015 |
Keywords
- 12J10
- 16K20
- 19D45
- Primary 16W60
- Secondary 05C25
ASJC Scopus subject areas
- General Mathematics