On normal integral bases in ray class fields over imaginary quadratic fields

Cornelius Greither

Acta Arithmetica (1997)

  • Volume: 78, Issue: 4, page 315-329
  • ISSN: 0065-1036

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Cornelius Greither. "On normal integral bases in ray class fields over imaginary quadratic fields." Acta Arithmetica 78.4 (1997): 315-329. <http://eudml.org/doc/206953>.

@article{CorneliusGreither1997,
author = {Cornelius Greither},
journal = {Acta Arithmetica},
keywords = {normal bases; class groups; cyclotomic descent; prime ideal; ray class field; normal integral basis; Stickelberger ideals; PARI},
language = {eng},
number = {4},
pages = {315-329},
title = {On normal integral bases in ray class fields over imaginary quadratic fields},
url = {http://eudml.org/doc/206953},
volume = {78},
year = {1997},
}

TY - JOUR
AU - Cornelius Greither
TI - On normal integral bases in ray class fields over imaginary quadratic fields
JO - Acta Arithmetica
PY - 1997
VL - 78
IS - 4
SP - 315
EP - 329
LA - eng
KW - normal bases; class groups; cyclotomic descent; prime ideal; ray class field; normal integral basis; Stickelberger ideals; PARI
UR - http://eudml.org/doc/206953
ER -

References

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  1. [1] P. Cassou-Noguès and M. Taylor, Elliptic Functions and Rings of Integers, Progr. Math. 66, Birkhäuser, 1986. Zbl0621.12012
  2. [2] L. Childs, The group of unramified Kummer extensions of prime degree, Proc. London Math. Soc. 35 (1995), 407-422. Zbl0374.13002
  3. [3] E. J. Gómez Ayala, Bases normales d'entiers dans les extensions de Kummer de degré premier, J. Théor. Nombres Bordeaux 6 (1994), 95-116. 
  4. [4] E. J. Gómez Ayala, Structure galoisienne et corps de classes de rayon de conducteur 2, Acta Arith. 72 (1995), 375-383. 
  5. [5] E. J. Gómez Ayala und R. Schertz, Eine Bemerkung zur Galoismodulstruktur in Strahlklassenkörpern über imaginärquadratischen Zahlkörpern, J. Number Theory 44 (1993), 41-46. 
  6. [6] C. Greither and R. Miranda, Galois extensions of prime degree, J. Algebra 124 (1989), 354-366. Zbl0706.13008
  7. [7] L. McCulloh, A Stickelberger condition on Galois module structure for Kummer extensions of prime degree, in: Algebraic Number Fields (Durham Proceedings), A. Fröhlich (ed.), Academic Press, London, 1977, 561-588. 
  8. [8] L. McCulloh, Galois module structure of elementary abelian extensions, J. Algebra 82 (1983), 102-134. Zbl0508.12008
  9. [9] R. Schertz, Galoismodulstruktur und elliptische Funktionen, J. Number Theory 39 (1991), 285-326. 
  10. [10] L. Washington, Introduction to Cyclotomic Fields, Grad. Texts in Math. 83, Springer, 1982. 

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