# Analytic normal basis theorem

Victor Alexandru; Nicolae Popescu; Alexandru Zaharescu

Open Mathematics (2008)

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

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topVictor 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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- [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] 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] Andronescu S.C., On some subrings of ${\tilde{\mathbb{Q}}}_{p}$ , Rev. Roumanie Math. Pures Appl., 2003, 48, 343–351 Zbl1100.13033
- [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] 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] 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] Sen S., On automorphisms of local fields, Ann. of Math., 1969, 90, 33–46 http://dx.doi.org/10.2307/1970680 Zbl0199.36301
- [9] Tate J.T., p - divisible groups, Proc. Conf. Local Fields (1966 Driebergen), Springer, Berlin, 1967, 158–183

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