Geodesic
A GALOIS THEORY FOR THE FIELD EXTENSION K((X))/K
Glasgow mathematical journal, Tome 52 (2010) no. 3, pp. 447-451

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DOI

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.
DOI : 10.1017/S0017089510000339
Mots-clés : Primary 12F10, 13F25, 12J20, Secondary 12J10, 12E99, 12F99 
POPESCU, ANGEL; NASEEM, ASIM; POPESCU, NICOLAE. A GALOIS THEORY FOR THE FIELD EXTENSION K((X))/K. Glasgow mathematical journal, Tome 52 (2010) no. 3, pp. 447-451. doi: 10.1017/S0017089510000339
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     journal = {Glasgow mathematical journal},
     pages = {447--451},
     year = {2010},
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     doi = {10.1017/S0017089510000339},
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