Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2024 MCQ for Mathematics of Computation is 1.78.

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Normal integral bases for $A_4$ extensions of the rationals
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by Jean Cougnard;
Math. Comp. 75 (2006), 485-496
DOI: https://doi.org/10.1090/S0025-5718-05-01779-5
Published electronically: September 1, 2005

Abstract:

We give an algorithm for constructing normal integral bases of tame Galois extensions of the rationals with group $A_4$. Using earlier works we can do the same until degree $15$.
References
  • E. Artin, Questions de base minimale dans la théorie des nombres algébriques, Algèbre et Théorie des Nombres, Colloq. Internat. CNRS, no. 24, CNRS, Paris, 1950, pp. 19–20 (French). MR 42450
  • Albert Châtelet, Arithmétique des corps abéliens du troisième degré, Ann. Sci. École Norm. Sup. (3) 63 (1946), 109–160 (1947) (French). MR 20598, DOI 10.24033/asens.934
  • Jean Cougnard, Anneaux d’entiers stablement libres sur $\Bbb Z[H_8\times C_2]$, J. Théor. Nombres Bordeaux 10 (1998), no. 1, 163–201 (French, with English and French summaries). MR 1827291, DOI 10.5802/jtnb.224
  • Jean Cougnard, Construction de base normale pour les extensions de $\textbf {Q}$ à groupe $D_4$, J. Théor. Nombres Bordeaux 12 (2000), no. 2, 399–409 (French, with English and French summaries). Colloque International de Théorie des Nombres (Talence, 1999). MR 1823192, DOI 10.5802/jtnb.286
  • Jean Cougnard and Jacques Queyrut, Construction de bases normales pour les extensions galoisiennes absolues à groupe de Galois quaternionien d’ordre 12, J. Théor. Nombres Bordeaux 14 (2002), no. 1, 87–102 (French, with English and French summaries). MR 1925992, DOI 10.5802/jtnb.348
  • Charles W. Curtis and Irving Reiner, Methods of representation theory. Vol. II, Pure and Applied Mathematics (New York), John Wiley & Sons, Inc., New York, 1987. With applications to finite groups and orders; A Wiley-Interscience Publication. MR 892316
  • Jacques Martinet, Sur l’arithmétique des extensions galoisiennes à groupe de Galois diédral d’ordre $2p$, Ann. Inst. Fourier (Grenoble) 19 (1969), no. fasc. 1, 1–80, ix (French, with English summary). MR 262210, DOI 10.5802/aif.307
  • C. BATUT, K. BELABAS, D. BERNARDI, H. COHEN, and M. OLIVIER. User’s Guide to Pari-GP, version 2.02.12 (1999).
  • Jean-Jacques Payan, Critère de décomposition d’une extension de Kummer sur un sous-corps du corps de base, Ann. Sci. École Norm. Sup. (4) 1 (1968), 445–458 (French). MR 237472, DOI 10.24033/asens.1169
  • Dock Sang Rim, Modules over finite groups, Ann. of Math. (2) 69 (1959), 700–712. MR 104721, DOI 10.2307/1970033
  • I. Reiner and S. Ullom, Remarks on class groups of integral group rings, Symposia Mathematica, Vol. XIII (Convegno di Gruppi Abeliani & Convegno di Gruppi e loro Rappresentazioni, INDAM, Rome, 1972) Academic Press, London-New York, 1974, pp. 501–516. MR 367043
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Bibliographic Information
  • Received by editor(s): March 28, 2004
  • Received by editor(s) in revised form: October 28, 2004
  • Published electronically: September 1, 2005
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 75 (2006), 485-496
  • MSC (2000): Primary 11R04, 11Y40; Secondary 11R33
  • DOI: https://doi.org/10.1090/S0025-5718-05-01779-5
  • MathSciNet review: 2176411