Some elementary remarks about n -local fields

Victor Alexandru; Nicolae Popescu

Rendiconti del Seminario Matematico della Università di Padova (1994)

  • Volume: 92, page 17-28
  • ISSN: 0041-8994

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Alexandru, Victor, and Popescu, Nicolae. "Some elementary remarks about $n$-local fields." Rendiconti del Seminario Matematico della Università di Padova 92 (1994): 17-28. <http://eudml.org/doc/108334>.

@article{Alexandru1994,
author = {Alexandru, Victor, Popescu, Nicolae},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {valued field; -local valued field},
language = {eng},
pages = {17-28},
publisher = {Seminario Matematico of the University of Padua},
title = {Some elementary remarks about $n$-local fields},
url = {http://eudml.org/doc/108334},
volume = {92},
year = {1994},
}

TY - JOUR
AU - Alexandru, Victor
AU - Popescu, Nicolae
TI - Some elementary remarks about $n$-local fields
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1994
PB - Seminario Matematico of the University of Padua
VL - 92
SP - 17
EP - 28
LA - eng
KW - valued field; -local valued field
UR - http://eudml.org/doc/108334
ER -

References

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  1. [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. Zbl0689.12017MR981094
  2. [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. Zbl0728.12009MR1068787
  3. [3] N. Bourbaki, Algebre commutative, Ch. V, VI, Hermann, Paris (1964). MR194450
  4. [4] H. Hasse, Number Theory, Springer, Berlin-Heidelberg-New York (1980). Zbl0423.12002MR562104
  5. [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. Zbl57.0169.01JFM57.0169.01
  6. [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. Zbl0143.06403MR225756
  7. [7] W. Krull, Allgemaine Bewertungstheorie, J. Math., 167 (1932), pp. 160-196. JFM58.0148.02
  8. [8] A.N. Parshin, Abelian coverings of arithmetic schemes (russian), Dokl. Acad. Nauk. SSSR, 243 (4) (1978), pp. 855-858. Zbl0443.12006MR514485
  9. [9] A.N. Parschin, Local class field theory (russian), Trudi Math. Inst. Steklov, 165 (1984), pp. 143-170. Zbl0535.12013MR752939
  10. [10] N. Popescu - A. Zaharescu, On valuations on k(X, Y) trivial on k, to appear. 
  11. [11] P. Samuel - O. Zariski, Commutative Algebra - II, Van Nostrand, Prince-ton (1960). Zbl0121.27801MR120249
  12. [12] O.F. Schilling, The theory of valuations, A.M.S. Math. Surveys, No. 4, Providence, Rhode Island (1950). Zbl0037.30702
  13. [13] J.P. Serre, Corp locaux, Hermann, Paris (1962). Zbl0137.02601
  14. [14] P. Teichmüller, Diskret bewertete perfecte Körper mit unvollkommenen Restklassenkörper, J. Math., 176 (1936), pp. 141-152. Zbl0016.05103JFM62.1114.01
  15. [15] E. Weiss, Algebraic Number Theory, McGraw-Hill Book Company, New York (1963). Zbl0115.03601MR159805

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