On Rayner structures

Abstract

In this note, we study substructures of generalized power series fields induced by families of well-ordered subsets of the group of exponents. We characterize the set-theoretic and algebraic properties of the induced substructures in terms of conditions on the families. We extend the work of Rayner by giving both necessary and sufficient conditions to obtain truncation closed subgroups, subrings and subfields.

Keywords:

• Formal power series
• ordered structures
• valuation theory

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 13J05
• 12J20
• 16W60
• 06F20

Acknowledgments

We thank Mickaël Matusinski for several helpful comments and corrections.