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A characterization of arithmetical invariants by the monoid of relations

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Abstract

The investigation and classification of non-unique factorization phenomena have attracted some interest in recent literature. For finitely generated monoids, S.T. Chapman and P. García-Sánchez, together with several co-authors, derived a method to calculate the catenary and tame degree from the monoid of relations, and they applied this method successfully in the case of numerical monoids. In this paper, we investigate the algebraic structure of this approach. Thereby, we dispense with the restriction to finitely generated monoids and give applications to other invariants of non-unique factorizations, such as the elasticity and the set of distances.

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Authors and Affiliations

  1. Institute for Mathematics and Scientific Computing, University Graz, Heinrichstrasse 36, 8010, Graz, Austria

    Andreas Philipp

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  1. Andreas Philipp
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Correspondence to Andreas Philipp.

Additional information

Communicated by László Márki.

This work was supported by the FWF Austrian Science Found (FWF Grant P18779-N13).

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Philipp, A. A characterization of arithmetical invariants by the monoid of relations. Semigroup Forum 81, 424–434 (2010). https://doi.org/10.1007/s00233-010-9218-1

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  • DOI: https://doi.org/10.1007/s00233-010-9218-1

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