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Arithmetic of block monoids. (English) Zbl 1108.11084
Summary: We investigate block monoids, the monoid of zero-sum sequences, over abelian groups and their divisor-closed submonoids. We derive some results that can be used as tools when investigating the arithmetic of such monoids. Moreover, we investigate block monoids over so-called simple sets, the somehow simplest kind of sets with the property that the block monoids have non-unique factorization.

##### MSC:
 11R27 Units and factorization 20K99 Abelian groups 13F05 Dedekind, Prüfer, Krull and Mori rings and their generalizations
##### Keywords:
block monoid; factorization; Krull monoid; zero-sum sequence
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##### References:
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