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A GALOIS THEORY FOR THE FIELD EXTENSION K((X))/K

Published online by Cambridge University Press:  25 August 2010

ANGEL POPESCU ,
ASIM NASEEM  and
NICOLAE POPESCU
ANGEL POPESCU
Affiliation:
Technical University of Civil Engineering Bucharest, Department of Mathematics and Computer Science, B-ul Lacul Tei 124, 020396 Bucharest 38, Romania e-mail: angel.popescu@gmail.com
ASIM NASEEM
Affiliation:
Abdus Salam School of Mathematical Sciences, Government College University, 68-B, New Muslim Town, Lahore 54600, Pakistan e-mail: asimroz@gmail.com
NICOLAE POPESCU
Affiliation:
Mathematical Institute of the Romanian Academy, P.O. Box 1-764, 70700 Bucharest, Romania e-mail: Nicolae.Popescu@imar.ro
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Abstract

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Let K be a field of characteristic 0, which is algebraically closed to radicals. Let F = K((X)) be the valued field of Laurent power series and let G = Aut(F/K). We prove that if L is a subfield of F, K ≠ L, such that L/K is a sub-extension of F/K and F/L is a Galois algebraic extension (L/K is Galois coalgebraic in F/K), then L is closed in F, F/L is a finite extension and Gal(F/L) is a finite cyclic group of G. We also prove that there is a one-to-one and onto correspondence between the set of all finite subgroups of G and the set of all Galois coalgebraic sub-extensions of F/K. Some other auxiliary results which are useful by their own are given.

Keywords

Primary 12F1013F2512J20Secondary 12J1012E9912F99
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 52 , Issue 3 , September 2010 , pp. 447 - 451
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

References

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