L'Innocente, S and Mantova, V orcid.org/0000-0002-8454-7315 (2017) Factorisation of germ-like series. Journal of Logic and Analysis, 9. 3. ISSN 1759-9008
Abstract
A classical tool in the study of real closed fields are the fields K((G)) of generalised power series (i.e., formal sums with well-ordered support) with coefficients in a field K of characteristic 0 and exponents in an ordered abelian group G. A fundamental result of Berarducci ensures the existence of irreducible series in the subring K((G≤0)) of K((G)) consisting of the generalised power series with non-positive exponents. It is an open question whether the factorisations of a series in such subring have common refinements, and whether the factorisation becomes unique after taking the quotient by the ideal generated by the non-constant monomials. In this paper, we provide a new class of irreducibles and prove some further cases of uniqueness of the factorisation.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This work is licensed under a Creative Commons Attribution 3.0 License. |
Keywords: | generalised power series, unique factorisation, order-value |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 24 Apr 2017 11:10 |
Last Modified: | 23 Jun 2023 22:27 |
Status: | Published |
Publisher: | University of Hawaii, Department of Mathematics |
Identification Number: | 10.4115/jla.2017.9.3 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:115383 |