Completely normal elements in some finite abelian extensions

 Access to full text

 Full (PDF)

1. [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. [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. [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. [4] Hachenberger D., Finite Fields, Kluwer Internat. Ser. Engrg. Comput. Sci., 390, Kluwer, Boston, 1997 
5. [5] Hachenberger D., Universal normal bases for the abelian closure of the field of rational numbers, Acta Arith., 2000, 93(4), 329–341 Zbl0956.11024
6. [6] Janusz G.J., Algebraic Number Fields, 2nd ed., Grad. Stud. Math., 7, American Mathematical Society, Providence, 1996 Zbl0854.11001
7. [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] Zbl1279.11061
8. [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. [9] Kubert D., Lang S., Modular Units, Grundlehren Math. Wiss., 244, Spinger, New York-Berlin, 1981 
10. [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. [11] Okada T., On an extension of a theorem of S. Chowla, Acta Arith., 1980/81, 38(4), 341–345 [WoS] 
12. [12] Shimura G., Introduction to the Arithmetic Theory of Automorphic Functions, Publ. Math. Soc. Japan, 11, Iwanami Shoten/Princeton University Press, Tokyo/Princeton, 1971 Zbl0221.10029
13. [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. [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]