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

2011/04/02 by Andreas Philipp, Philipp, Andreas · 1 citation
Computer Science · #11T55 #13A05 #13F15 #20M13 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1104.0293

openalex publication_date 2011/04/02 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

The investigation and classification of non-unique factorization phenomena\nhas attracted some interest in recent literature. For finitely generated\nmonoids, S.T. Chapman and P.A. Garc 'ia-S 'anchez, together with several\nco-authors, derived a method to calculate the catenary and tame degree from the\nmonoid of relations. Then, in [1], the algebraic structure of this approach was\ninvestigated and the restriction to finitely generated monoids was removed. We\nnow extend these ideas further to the monotone catenary degree and then apply\nall these results to the explicit computation of arithmetical invariants of\nsemigroup rings.\n [1] A. Philipp. A characterization of arithmetical invariants by the monoid\nof relations. Semigroup Forum, 81:424-434, 2010.\n

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• Factorization in Finitely-Presented Monoids

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