The tame degree and related invariants of non-unique factorizations
Local tameness and the finiteness of the catenary degree are two crucial finiteness conditions in the theory of non-unique factorizations in monoids and integral domains. In this note, we refine the notion of local tameness and relate the resulting invariants with the usual tame degree and the -invariant. Finally we present a simple monoid which fails to be locally tame and yet has nice factorization properties.