The Catenary and Tame Degree in Finitely Generated Commutative Cancellative Monoids

摘要

Problems involving chains of irreducible factorizations in atomic integral domains and monoids have been the focus of much recent literature. If S is a commutative cancellative atomic monoid, then the catenary degree of S (denoted c(S)) and the tame degree of S (denoted t(S)) are combinatorial invariants of S which describe the behavior of chains of factorizations. In this note, we describe methods to compute both c(S) and t(S) when M is a finitely generated commutative cancellative monoid.