| Title:
|
The algebraic closure of a $p$-adic number field is a complete topological field (English) |
| Author:
|
Marcos, José E. |
| Language:
|
English |
| Journal:
|
Mathematica Slovaca |
| ISSN:
|
0139-9918 |
| Volume:
|
56 |
| Issue:
|
3 |
| Year:
|
2006 |
| Pages:
|
317-331 |
| . |
| Category:
|
math |
| . |
| MSC:
|
12J99 |
| idZBL:
|
Zbl 1141.12002 |
| idMR:
|
MR2250083 |
| . |
| Date available:
|
2009-09-25T14:32:36Z |
| Last updated:
|
2012-08-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/136929 |
| . |
| Reference:
|
[1] ALEXANDRU V.-POPESCU N.-ZAHARESCU A.: On the closed subfields of $C^p$.J. Number Theory 68 (1998), 131-150. MR 1605907 |
| Reference:
|
[2] AMICE Y.: Les nombres p-adiques.Collection SUP. Le mathematicien 14, Presses Universitaires de France, Paris, 1975. Zbl 0313.12104, MR 0447195 |
| Reference:
|
[3] ARNAUTOV V. I.-GLAVATSKY S. T.-MIKHALEV A. V.: Introduction to the Theory of Topological Rings and Modules.Marcel Dekker, New York, 1996. Zbl 0842.16001, MR 1368852 |
| Reference:
|
[4] GOUVEA F. Q.: p-Adic Numbers: An Introduction (2nd ed.).Springer-Verlag, New York, 1997. Zbl 0874.11002, MR 1488696 |
| Reference:
|
[5] IOVITA A.-ZAHARESCU A.: Completions of r. a.t.-valued fields of rational functions.J. Number Theory 50 (1995), 202-205. Zbl 0813.12006, MR 1316815 |
| Reference:
|
[6] KOBLITZ N.: p-Adic Numbers, p-Adic Analysis, and Zeta-Functions (2nd ed.).Springer-Verlag, New York, 1984. MR 0754003 |
| Reference:
|
[7] LAMPERT D.: Algebraic p-adic expansions.J. Number Theory 23 (1986), 279-284. Zbl 0586.12021, MR 0846958 |
| Reference:
|
[8] MARCOS J. E.: Lacunar ring topologies and maximum ring topologies with a prescribed convergent sequence.J. Pure Appl. Algebra 162 (2001), 53-85. Zbl 1094.13542, MR 1844809 |
| Reference:
|
[9] MARCOS J. E.: Locally unbounded topological fields with topological nilpoients.Fund. Math. 173 (2002), 21-32. MR 1899045 |
| Reference:
|
[10] MARCOS J. E.: Erratum to Locally unbounded topological fields with topological nilpotents.Fund. Math. 176 (2003), 95-96. MR 1971474 |
| Reference:
|
[11] MURTY M. R.: Introduction to p-Adic Analityc Number Theory.Amer. Math. Soc, Providence, RI, 2002. MR 1913413 |
| Reference:
|
[12] MUTYLIN A. F.: Connected, complete, locally bounded fields. Complete not locally bounded fields.Math. USSR Sbornik 5 (1968), 433-449 [Translated from: Mat. Sb. 76 (1968), 454-472]. Zbl 0181.32701, MR 0230705 |
| Reference:
|
[13] POONEN B.: Maximally complete fields.Enseign. Math. 39 (1993), 87-106. Zbl 0807.12006, MR 1225257 |
| Reference:
|
[14] ROBERT A.M.: A Course in p-Adic Analysis.Springer-Verlag, New York, 2000. Zbl 0947.11035, MR 1760253 |
| Reference:
|
[15] SHELL N.: Topological Fields and Near Valuations.Marcel Dekker, New York, 1990. Zbl 0702.12003, MR 1075419 |
| Reference:
|
[16] SCHIKHOF W. H.: Ultrametric Calculus. An introduction to p-adic analysis.Cambridge Studies in Advanced Mathematics 4, Cambridge University Press, Cambridge, 1984. Zbl 0553.26006, MR 0791759 |
| Reference:
|
[17] WIESLAW W.: Topological Fields.Marcel Dekker, New York, 1988. Zbl 0661.12011, MR 0957508 |
| Reference:
|
[18] ZELENYUK E. G.-PROTASOV I. V.: Topologies on abelian groups.Math. USSR Izvestiya 37 (1991), 445-460. Zbl 0728.22003, MR 1086087 |
| Reference:
|
[19] ZELENYUK E. G.-PROTASOV I. V.-KHROMULYAK O. M.: Topologies on countable groups and rings.Dokl. Akad. Nauk Ukrain. SSR 182 no. 8 (1991), 8-11. (Russian) MR 1151523 |
| . |
