Abstract
In the last two decades new techniques emerged to construct valuations on an infinite division ring D, given a normal subgroup \({N \subseteq D^\times}\) 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.
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Ido Efrat: This research was supported by the Israel Science Foundation (Grant No. 152/13). Andrei S. Rapinchuk: Partially supported by NSF Grant DMS-1301800 and BSF Grant 201049.
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Efrat, I., Rapinchuk, A.S. & Segev, Y. On graphs and valuations. manuscripta math. 146, 395–432 (2015). https://doi.org/10.1007/s00229-014-0699-1
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DOI: https://doi.org/10.1007/s00229-014-0699-1