Universal normal bases for the abelian closure of the field of rational numbers
Dirk Hachenberger
Acta Arithmetica, Tome 92 (2000), p. 329-341 / Harvested from The Polish Digital Mathematics Library
Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:207417
@article{bwmeta1.element.bwnjournal-article-aav93i4p329bwm,
     author = {Dirk Hachenberger},
     title = {Universal normal bases for the abelian closure of the field of rational numbers},
     journal = {Acta Arithmetica},
     volume = {92},
     year = {2000},
     pages = {329-341},
     zbl = {0956.11024},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav93i4p329bwm}
}
Dirk Hachenberger. Universal normal bases for the abelian closure of the field of rational numbers. Acta Arithmetica, Tome 92 (2000) pp. 329-341. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav93i4p329bwm/

[000] [BlJo1] D. Blessenohl und K. Johnsen, Eine Verschärfung des Satzes von der Normalbasis, J. Algebra 103 (1986), 141-159. | Zbl 0607.12011

[001] [BlJo2] D. Blessenohl und K. Johnsen, Stabile Teilkörper galoisscher Erweiterungen und ein Problem von C. Faith, Arch. Math. (Basel) 56 (1991), 245-253. | Zbl 0706.12003

[002] [Bo] W. Bosma, Canonical bases for cyclotomic fields, Appl. Algebra Engrg. Comm. Comput. 1 (1990), 125-134. | Zbl 0741.11041

[003] [Br] T. Breuer, Integral bases for subfields of cyclotomic fields, ibid. 8 (1997), 279-289. | Zbl 0879.11057

[004] [Fa] C. C. Faith, Extensions of normal bases and completely basic fields, Trans. Amer. Math. Soc. 85 (1957), 406-427. | Zbl 0081.03502

[005] [Ha] D. Hachenberger, Finite Fields: Normal Bases and Completely Free Elements, Kluwer, Boston, 1997. | Zbl 0864.11065

[006] [Jo] K. Johnsen, Lineare Abhängigkeiten von Einheitswurzeln, Elem. Math. 40 (1985), 57-59.

[007] [Le] H. W. Lenstra, Jr., A normal basis theorem for infinite Galois extensions, Indag. Math. 47 (1985), 221-228. | Zbl 0569.12013

[008] [Ri] P. Ribenboim, Algebraic Numbers, Pure Appl. Math. 27, Wiley, New York, 1972.

[009] [Sche] A. Scheerhorn, Trace- and norm-compatible extensions of finite fields, Appl. Algebra Engrg. Comm. Comput. 3 (1992), 435-447.

[010] [Wa] L. C. Washington, Introduction to Cyclotomic Fields, Grad. Texts in Math. 83, Springer, Berlin, 1982.