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L'Innocente, S. and Mantova, V. orcid.org/0000-0002-8454-7315 (2024) A factorisation theory for generalised power series and omnific integers. Advances in Mathematics, 442. 109513. ISSN 0001-8708
Abstract
We prove that in every ring of generalised power series with non-positive real exponents and coefficients in a field of characteristic zero, every series admits a factorisation into finitely many irreducibles with infinite support, the number of which can be bounded in terms of the order type of the series, and a unique product, up to multiplication by a unit, of factors with finite support.
We deduce analogous results for the ring of omnific integers within Conway's surreal numbers, using a suitable notion of infinite product. In turn, we solve Gonshor's conjecture that the omnific integer is prime.
We also exhibit new classes of irreducible and prime generalised power series and omnific integers, generalising previous work of Berarducci and Pitteloud.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2024 The Authors. This is an open access article under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. |
Keywords: | Omnific integers, Surreal numbers, Pre-Schreier domain, Valued ring |
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: | 25 Jan 2024 11:41 |
Last Modified: | 09 Oct 2024 09:57 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.aim.2024.109513 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:208281 |
Available Versions of this Item
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Factorisation theorems for generalised power series. (deposited 25 Jan 2024 11:17)
- A factorisation theory for generalised power series and omnific integers. (deposited 25 Jan 2024 11:41) [Currently Displayed]