Equations over valued groups

2024/09/23 by Bagayoko, Vincent
#FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2409.14854

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.

Related

• Preordered groups and valued fields
• The algebraic theory of valued fields
• Pairs of valuations and the geometry of soluble groups
• Equations over direct powers of algebraic structures in relational languages
• Proof Theory and Ordered Groups