Previous |  Up |  Next


monoid; ideal; cancellative; torsion free
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.
[1] T.  Becker and W.  Weispfenning: Gröbner Bases: a Computational Approach to Commutative Algebra. Springer-Verlag, New York, 1993. MR 1213453
[2] A. H.  Clifford: The Algebraic Theory of Semigroups. Amer. Math. Soc., Providence, 1961. Zbl 0111.03403
[3] D.  Eisenbud and B.  Sturmfels: Binomial ideals. Duke Math. J. 84 (1996), 1–45. DOI 10.1215/S0012-7094-96-08401-X | MR 1394747
[4] R.  Gilmer: Commutative Semigroup Rings. University of Chicago Press, Chicago, 1984. MR 0741678 | Zbl 0566.20050
[5] J.  Herzog: Generators and relations of abelian semigroup and semigroups rings. Manuscripta Math. 3 (1970), 175–193. DOI 10.1007/BF01273309 | MR 0269762
[6] G. B. Preston: Rédei’s characterization of congruences of finitely generated free commutative semigroups. Acta Math. Acad. Sci. Hungar. 26 (1975), 337–342. DOI 10.1007/BF01902341 | MR 0473051
[7] L.  Rédei: The theory of finitely commutative semigroups. Pergamon, Oxford-Edinburgh-New York, 1965. MR 0188322
[8] J. C.  Rosales and P. A.  García-Sánchez: Finitely generated commutative monoids. vol. xiv, Nova Science Publishers, New York, 1999. MR 1694173
[9] 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. DOI 10.1080/00927879608825809 | MR 1414579
[10] J. C.  Rosales: On finitely generated submonoids of $N^k$. Semigroup Forum 50 (1995), 251–262. DOI 10.1007/BF02573522 | MR 1315517
[11] J. C.  Rosales and P. A.  García-Sánchez: Presentations for subsemigroups of finitely generated commutative semigroups. Israel J. Math. 113 (1999), 269–283. DOI 10.1007/BF02780180 | MR 1729450
Partner of
EuDML logo