Submission date: 7 April 2020

Abstract:

In this note, we study substructures of generalised power series fields induced by families of well-ordered subsets of the group of exponents. We relate set theoretic and algebraic properties of the families to algebraic features of the induced sets. By this, we extend the work of Rayner ('An algebraically closed field', 1968) to truncation closed substructures of generalised power series fields.

Mathematics Subject Classification: Primary: 13J05; Secondary: 12J20, 16W60, 06F20

Keywords and phrases: fields of generalised power series, Hahn fields, ordered abelian groups

Full text arXiv 2004.03239: pdf, ps.