Abstract
We study the semigroups isomorphic to principal ideals of finitely generated commutative monoids. We define the concept of finite presentation for this kind of semigroups. Furthermore, we show how to obtain information on these semigroups from their presentations.
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References
T. Becker and W. Weispfenning: Gröbner Bases: a Computational Approach to Commutative Algebra. Springer-Verlag, New York, 1993.
A. H. Clifford: The Algebraic Theory of Semigroups. Amer. Math. Soc., Providence, 1961.
D. Eisenbud and B. Sturmfels: Binomial ideals. Duke Math. J. 84 (1996), 1–45.
R. Gilmer: Commutative Semigroup Rings. University of Chicago Press, Chicago, 1984.
J. Herzog: Generators and relations of abelian semigroup and semigroups rings. Manuscripta Math. 3 (1970), 175–193.
G. B. Preston: Rédei's characterization of congruences of finitely generated free commutative semigroups. Acta Math. Acad. Sci. Hungar. 26 (1975), 337–342.
L. Rédei: The theory of finitely commutative semigroups. Pergamon, Oxford-Edinburgh-New York, 1965.
J.C. Rosales and P. A. García-Sánchez: Finitely generated commutative monoids. vol. xiv, Nova Science Publishers, New York, 1999.
J. C. Rosales and J. M. Urbano-Blanco: A deterministic algorithm to decide if a finitely presented monoid is cancellative. Comm. Algebra 24 (1996), 4217–4224.
J. C. Rosales: On finitely generated submonoids of ℕk. Semigroup Forum 50 (1995), 251–262.
J. C. Rosales and P. A. García-Sánchez: Presentations for subsemigroups of finitely generated commutative semigroups. Israel J. Math. 113 (1999), 269–283.
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Rosales, J.C., García-García, J.I. Principal ideals of finitely generated commutative monoids. Czechoslovak Mathematical Journal 52, 75–85 (2002). https://doi.org/10.1023/A:1021771304599
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DOI: https://doi.org/10.1023/A:1021771304599