Some elementary remarks about n-local fields
Alexandru, Victor ; Popescu, Nicolae
Rendiconti del Seminario Matematico della Università di Padova, Tome 92 (1994), p. 17-28 / Harvested from Numdam
@article{RSMUP_1994__92__17_0,
     author = {Alexandru, Victor and Popescu, Nicolae},
     title = {Some elementary remarks about $n$-local fields},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     volume = {92},
     year = {1994},
     pages = {17-28},
     mrnumber = {1320475},
     zbl = {0846.12006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RSMUP_1994__92__17_0}
}
Alexandru, Victor; Popescu, Nicolae. Some elementary remarks about $n$-local fields. Rendiconti del Seminario Matematico della Università di Padova, Tome 92 (1994) pp. 17-28. http://gdmltest.u-ga.fr/item/RSMUP_1994__92__17_0/

[1] V. Alexandru - N. POPESCU - A. ZAHARESCU, A theorem of characterization of residual transcendental extensions of a valuation, J. Math. Kyoto Univ., 18 (4) (1988), pp. 579-592. | MR 981094 | Zbl 0689.12017

[2] V. Alexandru - N. POPESCU - A. ZAHARESCU, Minimal pairs of definition of a residual transcendental extension of a valuation, J. Math. Kyoto Univ., 30 (2) (1990), pp. 207-225. | MR 1068787 | Zbl 0728.12009

[3] N. Bourbaki, Algebre commutative, Ch. V, VI, Hermann, Paris (1964). | MR 194450

[4] H. Hasse, Number Theory, Springer, Berlin-Heidelberg-New York (1980). | MR 562104 | Zbl 0423.12002

[5] K. Hensel, Arithmetische Theorie der algebraischen Functionen von zwei variablen. - I, II, J. Math., Band 165 (1931), pp. 257-264; Band 168 (1938), pp. 117-128. | JFM 57.0169.01

[6] M. Krasner, Nombre des extensions d'un degré donne d'un corps p-addique, in Le tendences géometriques en algèbre et théorie des nombre Clermont-Ferrand, 2-9 Avril 1964, (1966), pp. 143-169. | MR 225756 | Zbl 0143.06403

[7] W. Krull, Allgemaine Bewertungstheorie, J. Math., 167 (1932), pp. 160-196. | JFM 58.0148.02

[8] A.N. Parshin, Abelian coverings of arithmetic schemes (russian), Dokl. Acad. Nauk. SSSR, 243 (4) (1978), pp. 855-858. | MR 514485 | Zbl 0443.12006

[9] A.N. Parschin, Local class field theory (russian), Trudi Math. Inst. Steklov, 165 (1984), pp. 143-170. | MR 752939 | Zbl 0535.12013

[10] N. Popescu - A. Zaharescu, On valuations on k(X, Y) trivial on k, to appear.

[11] P. Samuel - O. Zariski, Commutative Algebra - II, Van Nostrand, Prince-ton (1960). | MR 120249 | Zbl 0121.27801

[12] O.F. Schilling, The theory of valuations, A.M.S. Math. Surveys, No. 4, Providence, Rhode Island (1950). | Zbl 0037.30702

[13] J.P. Serre, Corp locaux, Hermann, Paris (1962). | Zbl 0137.02601

[14] P. Teichmüller, Diskret bewertete perfecte Körper mit unvollkommenen Restklassenkörper, J. Math., 176 (1936), pp. 141-152. | JFM 62.1114.01

[15] E. Weiss, Algebraic Number Theory, McGraw-Hill Book Company, New York (1963). | MR 159805 | Zbl 0115.03601