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Mathematics of Computation

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Structure of Gröbner bases with respect to block orders

Authors: M'Hammed El Kahoui and Said Rakrak
Journal: Math. Comp. 76 (2007), 2181-2187
MSC (2000): Primary 13P10, 12Y05
Published electronically: April 17, 2007
MathSciNet review: 2336290
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Abstract: In this paper we study the structure of Gröbner bases with respect to block orders. We extend Lazard's theorem and the Gianni-Kalkbrenner theorem to the case of a zero-dimensional ideal whose trace in the ring generated by the first block of variables is radical. We then show that they do not hold for general zero-dimensional ideals.

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M'Hammed El Kahoui
Affiliation: Max-Planck-Institut für Informatik, Stuhlsatzenhausweg 85, 66123 Saarbrücken, Germany
Address at time of publication: Department of Mathematics, Faculty of Sciences Semlalie, Cadi Ayyad University, P.O. Box 2390, Marrakech, Morocco

Said Rakrak
Affiliation: Department of Mathematics and Computer Science, Faculty of Sciences and Techniques, Cadi Ayyad University, P.O. Box 549 Marrakech, Morocco

Keywords: Gr\"obner basis, Lazard structure theorem, Gianni-Kalkbrenner structure theorem.
Received by editor(s): October 28, 2004
Received by editor(s) in revised form: March 22, 2006
Published electronically: April 17, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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