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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Indispensable binomials in semigroup ideals


Authors: Ignacio Ojeda and Alberto Vigneron-Tenorio
Journal: Proc. Amer. Math. Soc. 138 (2010), 4205-4216
MSC (2010): Primary 13F20; Secondary 16W50, 13F55
Published electronically: June 30, 2010
MathSciNet review: 2680047
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Abstract: In this paper, we deal with the problem of the uniqueness of a minimal system of binomial generators of a semigroup ideal. Concretely, we give different necessary and/or sufficient conditions for the uniqueness of such a minimal system of generators. These conditions come from the study and combinatorial description of the so-called indispensable binomials in the semigroup ideal.


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Additional Information

Ignacio Ojeda
Affiliation: Departamento de Matemáticas, Universidad de Extremadura, E-06071 Badajoz, Spain
Email: ojedamc@unex.es

Alberto Vigneron-Tenorio
Affiliation: Departamento de Matemáticas, Universidad de Cádiz, E-11405 Jerez de la Frontera, Spain
Email: alberto.vigneron@uca.es

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10456-2
PII: S 0002-9939(2010)10456-2
Keywords: Semigroup ideal, indispensable binomial, minimal system of generators, Markov basis, simplicial complex, toric ideal, monomial algebra
Received by editor(s): October 23, 2009
Received by editor(s) in revised form: February 22, 2010
Published electronically: June 30, 2010
Additional Notes: Both authors are partially supported by the project MTM2007-64704, National Plan I+D+I. The first author is partially supported by Junta de Extremadura (ayuda a grupos GRU09104) and FEDER funds
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.