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

Voir la notice de l'article provenant de la source Cambridge University Press

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
@article{10_1017_S0017089510000339,
     author = {POPESCU, ANGEL and NASEEM, ASIM and POPESCU, NICOLAE},
     title = {A {GALOIS} {THEORY} {FOR} {THE} {FIELD} {EXTENSION} {K((X))/K}},
     journal = {Glasgow mathematical journal},
     pages = {447--451},
     year = {2010},
     volume = {52},
     number = {3},
     doi = {10.1017/S0017089510000339},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000339/}
}
TY  - JOUR
AU  - POPESCU, ANGEL
AU  - NASEEM, ASIM
AU  - POPESCU, NICOLAE
TI  - A GALOIS THEORY FOR THE FIELD EXTENSION K((X))/K
JO  - Glasgow mathematical journal
PY  - 2010
SP  - 447
EP  - 451
VL  - 52
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000339/
DO  - 10.1017/S0017089510000339
ID  - 10_1017_S0017089510000339
ER  - 
%0 Journal Article
%A POPESCU, ANGEL
%A NASEEM, ASIM
%A POPESCU, NICOLAE
%T A GALOIS THEORY FOR THE FIELD EXTENSION K((X))/K
%J Glasgow mathematical journal
%D 2010
%P 447-451
%V 52
%N 3
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000339/
%R 10.1017/S0017089510000339
%F 10_1017_S0017089510000339

[1] 1.Artin, E., Algebraic Numbers and Algebraic Functions (Gordon and Breach, Sciences Publishers, New York, 1967). Google Scholar

[2] 2.Dummit, D. S. and Foote, R. M., Abstract Algebra, 2nd edn. (John Wiley & Sons, Inc. New York, 2003). Google Scholar

[3] 3.Neukirch, J., Algebraic Number Theory (Springer Verlag, Berlin, 1999). Google Scholar | DOI

[4] 4.Roquette, P., On the History of Valuation Theory, Part I in Valuation Theory and its Applications, Vol. I (Kuhlmann, F. V., Kuhlmann, S. and Marshal, M., Editors), (Fields Institute Communications, AMS, New York, 2002), 291–355. Google Scholar

[5] 5.Schilling, O. F. G., Automorphisms of fields of formal power series, Bull. Amer. Math. Soc. 50 (12) (1944), 892–901. Google Scholar | DOI

[6] 6.Schmidt, F. K., Mehrfach perfekte Körper, Math. Ann. 108 (1933), 1–25. Google Scholar | DOI

[7] 7.Weiss, E., Algebraic Number Theory (McGraw-Hill Book Company, Inc., New York, 1963). Google Scholar

Cité par Sources :