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Commutative Cancellative Semigroups of Low Rank

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Abstract.

The rank of a commutative cancellative semigroup S is the cardinality of a maximal independent subset of S. In another communication we have characterized commutative cancellative semigroups of finite rank in several ways. We classify here semigroups of rank 1 and 2 by characterizing them in particular according to their type, which consists of their structure semilattice whose vertices are labelled by the rank of the corresponding component and distinguishing monoids from the idempotent-free ones.

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Authors and Affiliations

  1. Departamento de Álgebra, Facultad de Ciencias, Universidad de Granada, 18071, Granada, Spain

    Antonio M. Cegarra

  2. 21420, Bol, Brač, Croatia

    Mario Petrich

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  1. Antonio M. Cegarra
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  2. Mario Petrich
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Correspondence to Antonio M. Cegarra.

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Received: June 10, 2008.

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Cegarra, A.M., Petrich, M. Commutative Cancellative Semigroups of Low Rank. Results. Math. 54, 41–52 (2009). https://doi.org/10.1007/s00025-009-0390-0

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  • DOI: https://doi.org/10.1007/s00025-009-0390-0

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