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arXiv · 1401.8213

On graphs and valuations

Ido Efrat·Andrei S. Rapinchuk·Yoav Segev
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Abstract

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

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Ido Efrat, Andrei S. Rapinchuk, Yoav Segev. 2014-08-27. On graphs and valuations. https://arxiv.org/abs/1401.8213

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