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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