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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MR Zbl
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.
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 
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/
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