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On Cohen-Macaulay and Gorenstein simplicial affine semigroups

Published online by Cambridge University Press:  20 January 2009

J. C. Rosales  and
Pedro A. García-Sánchez
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Abstract

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We give arithmetic characterizations which allow us to determine algorithmically when the semigroup ring associated to a simplicial affine semigroup is Cohen-Macaulay and/or Gorenstein. These characterizations are then used to provide information about presentations of this kind of semigroup and, in particular, to obtain bounds for the cardinality of their minimal presentations. Finally, we show that these bounds are reached for semigroups with maximal codimension.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 41 , Issue 3 , October 1998 , pp. 517 - 537
Copyright
Copyright © Edinburgh Mathematical Society 1998

References

REFERENCES

1. Apéry, R., Sur les branches superlinéaires des courbes algébriques, C. R. Acad. Sci. Paris 222 (1946).Google Scholar
2. Goto, S., Suzuki, N. and Watanabe, K., On affine semigroup rings, Japan J. Math. 2 (1976), 1–12.CrossRefGoogle Scholar
3. Herzog, J., Generators and relations of abelian semigroup and semigroup rings, Manuscripta Math. 3 (1970), 175–193.Google Scholar
4. Hochster, M., Rings of invariants of tori, Cohen-Macaulay rings generated by monomials, and polytopes, Ann. of Math. 96 (1972), 318–337.Google Scholar
5. Kamoi, Y., Defining ideals of Cohen-Macaulay semigroup rings, Comm. Algebra 20 (1992), 3163–3189.Google Scholar
6. Rosales, J. C., Function minimum associated to a congruence on integral n-tuple space, Semigroup Forum 51 (1995), 87–95.Google Scholar
7. Rosales, J. C., An algorithmic method to compute a minimal relation for any numerical semigroup, Internat. J. Algebra Comput. 6 (1996), 441–455.CrossRefGoogle Scholar
8. Rosales, J. C., On numerical semigroups, Semigroup Forum 52 (1996), 307–318.Google Scholar
9. Rosales, J. C., On symmetric numerical semigroups, J. Algebra 182 (1996), 422–434.Google Scholar
10. Rosales, J. C. and García-Sánchez, P. A., An algorithm to compute a minimal relation for affine semigroups, submitted.Google Scholar
11. Trung, N. V. and Hoa, L. T., Affine semigroups and Cohen-Macaulay rings generated by monomials. Trans. Amer. Math. Soc. 298 (1986), 145–167.CrossRefGoogle Scholar