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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo


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ISSN
2391-5455
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Volume 11, Issue 10

Issues

Volume 13 (2015)

Completely normal elements in some finite abelian extensions

Ja Koo / Dong Shin
  • Department of Mathematics, Hankuk University of Foreign Studies, Yongin-si, Gyeonggi-do, 449-791, Republic of Korea
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Published Online: 2013-07-20 | DOI: https://doi.org/10.2478/s11533-013-0280-2

Abstract

We present some completely normal elements in the maximal real subfields of cyclotomic fields over the field of rational numbers, relying on the criterion for normal element developed in [Jung H.Y., Koo J.K., Shin D.H., Normal bases of ray class fields over imaginary quadratic fields, Math. Z., 2012, 271(1–2), 109–116]. And, we further find completely normal elements in certain abelian extensions of modular function fields in terms of Siegel functions.

MSC: 11R18; 11F03; 12F05

Keywords: Cyclotomic extensions; Modular functions; Normal bases

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About the article

Published Online: 2013-07-20

Published in Print: 2013-10-01


Citation Information: Open Mathematics, Volume 11, Issue 10, Pages 1725–1731, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/s11533-013-0280-2.

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© 2013 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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