Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 43, No. 1, pp. 233-241 (2002)

Finitely Generated Weakly Reductive Commutative Semigroups

J. C. Rosales, J. I. Garcia-Garcia

Departamento de Algebra, Universidad de Granada, E-18071 Granada, Spain, e-mail:; e-mail:

Abstract: We give characterizations of the property of being weakly reductive for finitely generated commutative semigroups. As a consequence of these characterizations we obtain an algorithm for determining from a presentation of a finitely generated commutative semigroup whether it is weakly reductive. Furthermore, we present some connections between cancellative finitely generated commutative semigroups, Archimedean weakly reductive finitely generated commutative semigroups and $\cal N$-semigroups.

Classification (MSC2000): 20M14, 20M30

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