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A characterization of arithmetical invariants by the monoid of relations II: the monotone catenary degree and applications to semigroup rings

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Abstract

The investigation and classification of nonunique factorization phenomena has attracted some interest in recent literature. For finitely generated monoids, S.T. Chapman and P.A. García-Sánchez, together with several co-authors, derived a method to calculate the catenary and tame degree from the monoid of relations. Then, in Philipp (Semigroup Forum 81:424–434, 2010), the algebraic structure of this approach was investigated and the restriction to finitely generated monoids was removed. We now extend these ideas further to the monotone catenary degree and then apply all these results to the explicit computation of arithmetical invariants of semigroup rings.

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Acknowledgments

I thank my Ph.D. thesis advisors Prof. Franz Halter-Koch and Prof. Alfred Geroldinger for all the help, advice, and mathematical discussions during my thesis which led to all results in this article.

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  1. Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universität Graz, Heinrichstrasse 36, 8010, Graz, Austria

    Andreas Philipp

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  1. Andreas Philipp
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Correspondence to Andreas Philipp.

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Communicated by László Márki.

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Philipp, A. A characterization of arithmetical invariants by the monoid of relations II: the monotone catenary degree and applications to semigroup rings. Semigroup Forum 90, 220–250 (2015). https://doi.org/10.1007/s00233-014-9616-x

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