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

摘要

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. Garcia-Sanchez, 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.