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2013 | 11 | 10 | 1725-1731
Tytuł artykułu

Completely normal elements in some finite abelian extensions

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Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
10
Strony
1725-1731
Opis fizyczny
Daty
wydano
2013-10-01
online
2013-07-20
Twórcy
autor
autor
  • Department of Mathematics, Hankuk University of Foreign Studies, Yongin-si, Gyeonggi-do, 449-791, Republic of Korea, dhshin@hufs.ac.kr
Bibliografia
  • [1] Blessenohl D., Johnsen K., Eine Verschärfung des Satzes von der Normalbasis, J. Algebra, 1986, 103(1), 141–159 http://dx.doi.org/10.1016/0021-8693(86)90174-2[Crossref]
  • [2] Chowla S., The nonexistence of nontrivial linear relations between the roots of a certain irreducible equation, J. Number Theory, 1970, 2(1), 120–123 http://dx.doi.org/10.1016/0022-314X(70)90012-0[Crossref]
  • [3] Faith C.C., Extensions of normal bases and completely basic fields, Trans. Amer. Math. Soc., 1957, 85(2), 406–427 http://dx.doi.org/10.1090/S0002-9947-1957-0087632-7[Crossref]
  • [4] Hachenberger D., Finite Fields, Kluwer Internat. Ser. Engrg. Comput. Sci., 390, Kluwer, Boston, 1997
  • [5] Hachenberger D., Universal normal bases for the abelian closure of the field of rational numbers, Acta Arith., 2000, 93(4), 329–341
  • [6] Janusz G.J., Algebraic Number Fields, 2nd ed., Grad. Stud. Math., 7, American Mathematical Society, Providence, 1996
  • [7] 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 http://dx.doi.org/10.1007/s00209-011-0854-2[Crossref][WoS]
  • [8] Kawamoto F., On normal integral bases, Tokyo J. Math., 1984, 7(1), 221–231 http://dx.doi.org/10.3836/tjm/1270153005[Crossref]
  • [9] Kubert D., Lang S., Modular Units, Grundlehren Math. Wiss., 244, Spinger, New York-Berlin, 1981
  • [10] Lang S., Elliptic Functions, 2nd ed., Grad. Texts in Math., 112, Spinger, New York, 1987 http://dx.doi.org/10.1007/978-1-4612-4752-4[Crossref]
  • [11] Okada T., On an extension of a theorem of S. Chowla, Acta Arith., 1980/81, 38(4), 341–345 [WoS]
  • [12] Shimura G., Introduction to the Arithmetic Theory of Automorphic Functions, Publ. Math. Soc. Japan, 11, Iwanami Shoten/Princeton University Press, Tokyo/Princeton, 1971
  • [13] van der Waerden B.L., Algebra I, Springer, New York, 1991 http://dx.doi.org/10.1007/978-1-4684-9999-5[Crossref]
  • [14] Washington L.C., Introduction to Cyclotomic Fields, Grad. Texts in Math., 83, Springer, New York, 1982 http://dx.doi.org/10.1007/978-1-4684-0133-2[Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0280-2
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