Analytic normal basis theorem

Victor Alexandru; Nicolae Popescu; Alexandru Zaharescu

Open Mathematics (2008)

  • Volume: 6, Issue: 3, page 351-356
  • ISSN: 2391-5455

Abstract

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Let p be a prime number, ℚp the field of p-adic numbers, and ℚ ¯ p a fixed algebraic closure of ℚp. We provide an analytic version of the normal basis theorem which holds for normal extensions of intermediate fields ℚp ⊆ K ⊆ L ⊆ ℚ ¯ p .

How to cite

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Victor Alexandru, Nicolae Popescu, and Alexandru Zaharescu. "Analytic normal basis theorem." Open Mathematics 6.3 (2008): 351-356. <http://eudml.org/doc/269562>.

@article{VictorAlexandru2008,
abstract = {Let p be a prime number, ℚp the field of p-adic numbers, and \[ \bar\{\mathbb \{Q\}\}\_p \] a fixed algebraic closure of ℚp. We provide an analytic version of the normal basis theorem which holds for normal extensions of intermediate fields ℚp ⊆ K ⊆ L ⊆ \[ \bar\{\mathbb \{Q\}\}\_p \] .},
author = {Victor Alexandru, Nicolae Popescu, Alexandru Zaharescu},
journal = {Open Mathematics},
keywords = {p-adic fields; normal bases; Normal bases; -adic fields},
language = {eng},
number = {3},
pages = {351-356},
title = {Analytic normal basis theorem},
url = {http://eudml.org/doc/269562},
volume = {6},
year = {2008},
}

TY - JOUR
AU - Victor Alexandru
AU - Nicolae Popescu
AU - Alexandru Zaharescu
TI - Analytic normal basis theorem
JO - Open Mathematics
PY - 2008
VL - 6
IS - 3
SP - 351
EP - 356
AB - Let p be a prime number, ℚp the field of p-adic numbers, and \[ \bar{\mathbb {Q}}_p \] a fixed algebraic closure of ℚp. We provide an analytic version of the normal basis theorem which holds for normal extensions of intermediate fields ℚp ⊆ K ⊆ L ⊆ \[ \bar{\mathbb {Q}}_p \] .
LA - eng
KW - p-adic fields; normal bases; Normal bases; -adic fields
UR - http://eudml.org/doc/269562
ER -

References

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  1. [1] Alexandru V., Popescu E.L., Popescu N., On the continuity of the trace, Proc. Rom. Acad. Ser. A Math. Phys. Tech. Sci. Inf. Sci., 2004, 5, 117–122 Zbl1150.11438
  2. [2] Alexandru V., Popescu N., Zaharescu A., On the closed subfields of ℂp, J. Number Theory, 1998, 68, 131–150 http://dx.doi.org/10.1006/jnth.1997.2198 Zbl0901.11035
  3. [3] Alexandru V., Popescu N., Zaharescu A., Trace on ℂp, J. Number Theory, 2001, 88, 13–48 http://dx.doi.org/10.1006/jnth.2000.2610 
  4. [4] Andronescu S.C., On some subrings of ℚ ˜ p , Rev. Roumanie Math. Pures Appl., 2003, 48, 343–351 Zbl1100.13033
  5. [5] Ax J., Zeros of polynomials over local fields-The Galois action, J. Algebra, 1970, 15, 417–428 http://dx.doi.org/10.1016/0021-8693(70)90069-4 
  6. [6] Jacobson N., Lectures in abstract algebra Vol III: Theory of fields and Galois theory, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London-New York, 1964 Zbl0124.27002
  7. [7] Popescu N., Vâjâitu M., Zaharescu A., On the existence of trace for elements of ℂp, Algebr. Represent. Theory, 2006, 9, 47–66 http://dx.doi.org/10.1007/s10468-005-9003-0 Zbl1138.11054
  8. [8] Sen S., On automorphisms of local fields, Ann. of Math., 1969, 90, 33–46 http://dx.doi.org/10.2307/1970680 Zbl0199.36301
  9. [9] Tate J.T., p - divisible groups, Proc. Conf. Local Fields (1966 Driebergen), Springer, Berlin, 1967, 158–183 

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