Submission date: 20 January 2017

Abstract:

We give group analogs of two important theorems of real algebra concerning convex valuations, one of which is the Baer-Krull theorem. We do this by using quasi-orders, which gives a uniform approach to valued and ordered groups. We also recover the classical Baer-Krull theorem from its group analog.

Mathematics Subject Classification: 13A18, 12J20, 06F20

Keywords and phrases: valued fields, valued groups, ordered groups, quasi-orders, convex valuations, Baer-Krull theorem

Full text arXiv 1701.05827: pdf, ps.