The algebraic closure of a p -adic number field is a complete topological field

José E. Marcos

Mathematica Slovaca (2006)

  • Volume: 56, Issue: 3, page 317-331
  • ISSN: 0139-9918

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Marcos, José E.. "The algebraic closure of a $p$-adic number field is a complete topological field." Mathematica Slovaca 56.3 (2006): 317-331. <http://eudml.org/doc/34621>.

@article{Marcos2006,
author = {Marcos, José E.},
journal = {Mathematica Slovaca},
keywords = {topological field; -adic field},
language = {eng},
number = {3},
pages = {317-331},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {The algebraic closure of a $p$-adic number field is a complete topological field},
url = {http://eudml.org/doc/34621},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Marcos, José E.
TI - The algebraic closure of a $p$-adic number field is a complete topological field
JO - Mathematica Slovaca
PY - 2006
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 56
IS - 3
SP - 317
EP - 331
LA - eng
KW - topological field; -adic field
UR - http://eudml.org/doc/34621
ER -

References

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  5. IOVITA A.-ZAHARESCU A., Completions of r. a.t.-valued fields of rational functions, J. Number Theory 50 (1995), 202-205. (1995) Zbl0813.12006MR1316815
  6. KOBLITZ N., p-Adic Numbers, p-Adic Analysis, and Zeta-Functions (2nd ed.), Springer-Verlag, New York, 1984. (1984) MR0754003
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  8. MARCOS J. E., Lacunar ring topologies and maximum ring topologies with a prescribed convergent sequence, J. Pure Appl. Algebra 162 (2001), 53-85. Zbl1094.13542MR1844809
  9. MARCOS J. E., Locally unbounded topological fields with topological nilpoients, Fund. Math. 173 (2002), 21-32. MR1899045
  10. MARCOS J. E., Erratum to Locally unbounded topological fields with topological nilpotents, Fund. Math. 176 (2003), 95-96. MR1971474
  11. MURTY M. R., Introduction to p-Adic Analityc Number Theory, Amer. Math. Soc, Providence, RI, 2002. MR1913413
  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]. (1968) Zbl0181.32701MR0230705
  13. POONEN B., Maximally complete fields, Enseign. Math. 39 (1993), 87-106. (1993) Zbl0807.12006MR1225257
  14. ROBERT A.M., A Course in p-Adic Analysis, Springer-Verlag, New York, 2000. Zbl0947.11035MR1760253
  15. SHELL N., Topological Fields and Near Valuations, Marcel Dekker, New York, 1990. (1990) Zbl0702.12003MR1075419
  16. SCHIKHOF W. H., Ultrametric Calculus. An introduction to p-adic analysis, Cambridge Studies in Advanced Mathematics 4, Cambridge University Press, Cambridge, 1984. (1984) Zbl0553.26006MR0791759
  17. WIESLAW W., Topological Fields, Marcel Dekker, New York, 1988. (1988) Zbl0661.12011MR0957508
  18. ZELENYUK E. G.-PROTASOV I. V., Topologies on abelian groups, Math. USSR Izvestiya 37 (1991), 445-460. (1991) Zbl0728.22003MR1086087
  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) (1991) MR1151523

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