On Rayner structures
Commutative Algebra
2022-07-04 v4 Logic
Rings and Algebras
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.
Cite
@article{arxiv.2004.03239,
title = {On Rayner structures},
author = {Lothar Sebastian Krapp and Salma Kuhlmann and Michele Serra},
journal= {arXiv preprint arXiv:2004.03239},
year = {2022}
}
Comments
11 pages, to appear in Communications in Algebra