Geodesic
The tame degree and related invariants of non-unique factorizations
Communications in Mathematics, Tome 16 (2008) no. 1, pp. 57-68.

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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 $\omega $-invariant. Finally we present a simple monoid which fails to be locally tame and yet has nice factorization properties.
Classification : 13A05, 20M14
Keywords: Non-unique factorizations; tame degree; atomic monoids 
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Halter-Koch, Franz. The tame degree and related invariants of non-unique factorizations. Communications in Mathematics, Tome 16 (2008) no. 1, pp. 57-68. http://geodesic.mathdoc.fr/item/COMIM_2008__16_1_a5/