Fleischmann, Peter, Woodcock, Chris F. (2018) Stable transcendence for formal power series, generalized ArtinSchreier polynomials and a conjecture concerning pgroups. Bulletin of the London Mathematical Society, 50 (5). pp. 933944. ISSN 00246093. (doi:10.1112/blms.12197)
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Official URL https://doi.org/10.1112/blms.12197 
Abstract
Let f(x) be a formal power series with coefficients in the field k and let n ? 1. We define the notion of ntranscendence 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 Galoisalgebras of an elementary Abelian pgroup G, introduced in [2, 3, 4, 5]. Since the concept of ntranscendence is of independent interest in all characteristics, a number of fundamental theorems are proved where the generalized ArtinSchreier 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:  Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Pure Mathematics 
Depositing User:  Chris F Woodcock 
Date Deposited:  20 Aug 2018 15:27 UTC 
Last Modified:  28 Aug 2019 23:00 UTC 
Resource URI:  https://kar.kent.ac.uk/id/eprint/68722 (The current URI for this page, for reference purposes) 
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