Generalized Puiseux expansions and their Galois groups
type: Item
instance of: scholarly article
title: Generalized Puiseux expansions and their Galois groups
zbMATH Open document ID: 0904.12003
author: Sanju Vaidya
published in: Illinois Journal of Mathematics
publication date: 1997-08-18T00:00:00Z
review text: The author considers an algebraically closed field \(k\) of characteristic \(p\) and the field \(k((X^{\mathbb Q,p}))\) of the restricted power series over \(k\) [see \textit{P. Ribenboim}, Manuscr. Math. 75, 115-150 (1992; Zbl 0767.12001)]. He obtains criteria for special restricted power series to be algebraic over the field of meromorphic formal power series \(k((T))\). It is proved that if \(k\) is not the algebraic closure of its prime field, \(Y\in k\) is transcendental over the prime field of \(k\), \(L\) is a finite field contained in \(k\), \(f_i(Y)\in L[Y]\) and there exists a positive integer \(M\) such that \(\deg f_i(Y)\leq M\) for all \(i\), then the element \(f=\sum_{i=1}^\infty f_i(Y)X^{-1/p^i}\) is algebraic over \(k((X))\) if and only if it is periodical. Finally, the author computes the Galois groups of some particular restricted power series.
reviewed by: Doru Ştefănescu
Mathematics Subject Classification ID: 12F10
Mathematics Subject Classification ID: 13F25
Mathematics Subject Classification ID: 12F05
Mathematics Subject Classification ID: 20B25
zbMATH DE Number: 1029006
zbMATH Keywords: generalized power series
zbMATH Keywords: Galois groups
zbMATH Keywords: algebraic elements
zbMATH Keywords: periodical elements
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1029006