On graphs and valuations

الأصل · EN

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.