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Structure of Gröbner bases with respect to block orders
Author(s):
M'Hammed
El Kahoui;
Said
Rakrak.
Journal:
Math. Comp.
76
(2007),
2181-2187.
MSC (2000):
Primary 13P10, 12Y05
Posted:
April 17, 2007
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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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Additional Information:
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
Email:
elkahoui@mpi-sb.mpg.de
Said
Rakrak
Affiliation:
Department of Mathematics and Computer Science, Faculty of Sciences and Techniques, Cadi Ayyad University, P.O. Box 549 Marrakech, Morocco
Email:
rakrak@fstg-marrakech.ac.ma
DOI:
10.1090/S0025-5718-07-01972-2
PII:
S 0025-5718(07)01972-2
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
Posted:
April 17, 2007
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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