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Normal integral bases for extensions of the rationals
Author(s):
Jean
Cougnard.
Journal:
Math. Comp.
75
(2006),
485-496.
MSC (2000):
Primary 11R04, 11Y40;
Secondary 11R33
Posted:
September 1, 2005
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Abstract:
We give an algorithm for constructing normal integral bases of tame Galois extensions of the rationals with group . Using earlier works we can do the same until degree .
References:
-
- 1.
- E. ARTIN. Questions de base minimale dans la théorie des nombres algébriques, Colloque du C.N.R.S. Algèbre et Théorie des Nombres, Paris (1949) pp. 19-20. MR 0042450 (13,113i)
- 2.
- A. CHÂTELET. Arithmétique des corps abéliens du troisième degré, Ann. Sci. E.N.S. 63 (1946), 121-160. MR 0020598 (8:568a)
- 3.
- J. COUGNARD. Anneau d'entiers stablement libre sur
, Journal de Théorie des Nombres de Bordeaux 10 (1998), 163-201. MR 1827291 (2002a:11124) - 4.
- J. COUGNARD. Construction de base normale pour les extensions de
à groupe , Journal de Théorie des Nombres de Bordeaux 12 (2000), 399-409.MR 1823192 (2002d:11128) - 5.
- J. COUGNARD. and J. QUEYRUT. Construction de bases normales pour les extensions galoisiennes absolues à groupe de Galois quaternionien d'ordre
, Journal de Théorie des Nombres de Bordeaux 14 fas. 1 (2002), 87-102.MR 1925992 (2003k:11173) - 6.
- C.W. CURTIS and I. REINER. Methods of representation theory, with applications to finite groups and orders Vol. II, John Wiley and Sons (1987).MR 0892316 (88f:20002)
- 7.
- J. MARTINET. Sur l'arithmétique d'une extension galoisienne à groupe de Galois diédral d'ordre
Ann. Inst. Fourier 19 (1969), 1-80. MR 0262210 (41:6820) - 8.
- C. BATUT, K. BELABAS, D. BERNARDI, H. COHEN, and M. OLIVIER. User's Guide to Pari-GP, version 2.02.12 (1999).
- 9.
- J.-J. PAYAN. Critère de décomposition d'une extension de Kummer sur un sous-corps du corps de base, Ann. Sci. de l'E.N.S. 4e série 1 (1964), 445-458. MR 0237472 (38:5754)
- 10.
- D.S. RIM. Modules over finite groups Ann. Math. (2) 69 (1959), 700-712. MR 0104721 (21:3474)
- 11.
- I. REINER and S. ULLOM. Remarks on class groups of integral group rings, Symp. Math. Inst. Nazionale Alta Math. (Rome) 13 (1974), 501-506.MR 0367043 (51:3285)
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Additional Information:
DOI:
10.1090/S0025-5718-05-01779-5
PII:
S 0025-5718(05)01779-5
Keywords:
Number theory,
algorithm
Received by editor(s):
March 28, 2004
Received by editor(s) in revised form:
October 28, 2004
Posted:
September 1, 2005
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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