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On the class semigroup of a numerical semigroup

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Abstract

The class semigroup of a numerical semigroup \(S\) is the semigroup \(\mathcal {S}(S)\) of classes of the relative ideals of \(S\). Our aim is to find some properties of \(\mathcal {S}(S)\). In particular we observe that \(\mathcal {S}(S)\) is finite and compute its cardinality in some cases, using the poset of gaps of \(S\). Moreover, we study the generators of \(\mathcal {S}(S)\) and the reduction number of its elements.

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Acknowledgments

We would like to thank the referee for her/his careful reading and helpful suggestions.

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Authors and Affiliations

  1. Dipartimento di Matematica, Sapienza, Università di Roma, Piazzale A. Moro 2, 00185, Rome, Italy

    Valentina Barucci

  2. Department of Mathematics, Faculty of Sciences, 5000, Monastir, Tunisia

    Faten Khouja

Authors
  1. Valentina Barucci
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  2. Faten Khouja
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Corresponding author

Correspondence to Valentina Barucci.

Additional information

Communicated by Fernando Torres.

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Barucci, V., Khouja, F. On the class semigroup of a numerical semigroup. Semigroup Forum 92, 377–392 (2016). https://doi.org/10.1007/s00233-014-9679-8

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  • DOI: https://doi.org/10.1007/s00233-014-9679-8

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