On Rayner structures
arXiv:2004.03239 · doi:10.1080/00927872.2021.1976789
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 characterise 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 \emph{necessary} and sufficient conditions to obtain truncation closed subgroups, subrings and subfields.
11 pages, to appear in Communications in Algebra