Within the field of Laurent series with rational coefficients Q((t)), those series representing rational functions can be characterised via linear recurrence relations of their coefficients. Inspired by this result, we established a notion of generalised linear recurrence relations within fields of generalised power series k((G)), where k is a field and G is a totally ordered abelian group.

In this talk, we present distinguished algebraic substructures of k((G)) that are determined by generalised linear recurrence relations. These cover Rayner fields (see [1]), which consist of all power series in k((G)) whose support lies within a specific family of well-ordered subsets of G. Moreover, we provide construction methods for subfields of k((G)) exhibiting certain lifting properties, which are of particular interest in the study of automorphism groups of Hahn fields (see [2]).

References

[1] L. S. Krapp, S. Kuhlmann and M. Serra, On Rayner structures, Comm. Algebra 50 (2022) 940-948, doi:10.1080/00927872.2021.1976789.

[2] S. Kuhlmann and M. Serra, The automorphism group of a valued field of generalised power series, J. Algebra 605 (2022) 339-376, doi:10.1016/j.jalgebra.2022.04.023.