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# Article

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Keywords:
Non-unique factorizations; tame degree; atomic monoids
Summary:
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.
References:
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