Equations over valued groups

TL;DR

This paper explores algebraic and topological properties of groups with valuations, applying valuation theory to solve regular equations over groups.

Contribution

It introduces valuation-theoretic methods to analyze groups, exponential groups, and ordered groups, providing new tools for solving equations over groups.

Findings

Valuation structures reveal new algebraic properties.

Valuation methods simplify solving regular equations.

Topological features of valued groups are characterized.

Abstract

We study groups, exponential groups and ordered groups equipped with valuations. We investigate algebraic and topological features of such valued structures, and apply our findings in order to solve regular equations over groups using simple valuation theoretic arguments.