Universal normal bases for the abelian closure of the field of rational numbers

Dirk Hachenberger

Acta Arithmetica (2000)

  • Volume: 93, Issue: 4, page 329-341
  • ISSN: 0065-1036

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Dirk Hachenberger. "Universal normal bases for the abelian closure of the field of rational numbers." Acta Arithmetica 93.4 (2000): 329-341. <http://eudml.org/doc/207417>.

@article{DirkHachenberger2000,
author = {Dirk Hachenberger},
journal = {Acta Arithmetica},
keywords = {cyclotomic field; abelian closure; normal basis/element; universally normal basis/element; completely normal basis/element; trace-compatible sequence; normal basis},
language = {eng},
number = {4},
pages = {329-341},
title = {Universal normal bases for the abelian closure of the field of rational numbers},
url = {http://eudml.org/doc/207417},
volume = {93},
year = {2000},
}

TY - JOUR
AU - Dirk Hachenberger
TI - Universal normal bases for the abelian closure of the field of rational numbers
JO - Acta Arithmetica
PY - 2000
VL - 93
IS - 4
SP - 329
EP - 341
LA - eng
KW - cyclotomic field; abelian closure; normal basis/element; universally normal basis/element; completely normal basis/element; trace-compatible sequence; normal basis
UR - http://eudml.org/doc/207417
ER -

References

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  1. [BlJo1] D. Blessenohl und K. Johnsen, Eine Verschärfung des Satzes von der Normalbasis, J. Algebra 103 (1986), 141-159. Zbl0607.12011
  2. [BlJo2] D. Blessenohl und K. Johnsen, Stabile Teilkörper galoisscher Erweiterungen und ein Problem von C. Faith, Arch. Math. (Basel) 56 (1991), 245-253. Zbl0706.12003
  3. [Bo] W. Bosma, Canonical bases for cyclotomic fields, Appl. Algebra Engrg. Comm. Comput. 1 (1990), 125-134. Zbl0741.11041
  4. [Br] T. Breuer, Integral bases for subfields of cyclotomic fields, ibid. 8 (1997), 279-289. Zbl0879.11057
  5. [Fa] C. C. Faith, Extensions of normal bases and completely basic fields, Trans. Amer. Math. Soc. 85 (1957), 406-427. Zbl0081.03502
  6. [Ha] D. Hachenberger, Finite Fields: Normal Bases and Completely Free Elements, Kluwer, Boston, 1997. Zbl0864.11065
  7. [Jo] K. Johnsen, Lineare Abhängigkeiten von Einheitswurzeln, Elem. Math. 40 (1985), 57-59. 
  8. [Le] H. W. Lenstra, Jr., A normal basis theorem for infinite Galois extensions, Indag. Math. 47 (1985), 221-228. Zbl0569.12013
  9. [Ri] P. Ribenboim, Algebraic Numbers, Pure Appl. Math. 27, Wiley, New York, 1972. 
  10. [Sche] A. Scheerhorn, Trace- and norm-compatible extensions of finite fields, Appl. Algebra Engrg. Comm. Comput. 3 (1992), 435-447. 
  11. [Wa] L. C. Washington, Introduction to Cyclotomic Fields, Grad. Texts in Math. 83, Springer, Berlin, 1982. 

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