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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) (Access to this publication is currently restricted. You may be able to access a copy if URLs are provided)

 PDF - Author's Accepted Manuscript Restricted to Repository staff only until 28 August 2019. Contact us about this Publication Download (277kB) Official URLhttps://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 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 10.1112/blms.12197 Q Science > QA Mathematics (inc Computing science) Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Pure Mathematics Chris F Woodcock 20 Aug 2018 15:27 UTC 11 Jul 2019 13:18 UTC https://kar.kent.ac.uk/id/eprint/68722 (The current URI for this page, for reference purposes)
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