# A Baer-Krull theorem for quasi-ordered groups

## TL;DR

This paper extends the Baer-Krull theorem to quasi-ordered groups, providing a unified framework for valued and ordered groups and recovering classical results.

## Contribution

It introduces a group analog of the Baer-Krull theorem using quasi-orders, unifying valued and ordered group theories.

## Key findings

- Established a group version of the Baer-Krull theorem.
- Unified the treatment of valued and ordered groups via quasi-orders.
- Recovered classical Baer-Krull theorem from the group analog.

## 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.