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Stable transcendence for formal power series, generalized Artin-Schreier polynomials and a conjecture concerning p-groups

Fleischmann, Peter, Woodcock, Chris F. (2018) Stable transcendence for formal power series, generalized Artin-Schreier polynomials and a conjecture concerning p-groups. Bulletin of the London Mathematical Society, 50 (5). pp. 933-944. ISSN 0024-6093. (doi:10.1112/blms.12197) (KAR id:68722)

Abstract

Let f(x) be a formal power series with coefficients in the field k and let n ? 1. We define the notion of n-transcendence of f(x) over k and, more generally, the stable transcendence function dk(f(x), n). It is shown that, if k has prime characteristic p, this function determines the minimal Krull dimension dk(G) of the universal modular Galois-algebras of an elementary Abelian p-group G, introduced in [2, 3, 4, 5]. Since the concept of n-transcendence is of independent interest in all characteristics, a number of fundamental theorems are proved where the generalized Artin-Schreier polynomials surprisingly play a central role. We make a plausible conjecture in the case when k = Fp, the truth of which would imply a conjectural result concerning dFp (G) previously investigated by the authors.

Item Type: Article
DOI/Identification number: 10.1112/blms.12197
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Christopher Woodcock
Date Deposited: 20 Aug 2018 15:27 UTC
Last Modified: 09 Dec 2022 03:59 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/68722 (The current URI for this page, for reference purposes)

University of Kent Author Information

Fleischmann, Peter.

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CReDIT Contributor Roles:

Woodcock, Chris F..

Creator's ORCID: https://orcid.org/0000-0003-4713-0040
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