On the arithmetic of Krull monoids with infinite cyclic class group

Details On the arithmetic of Krull monoids with infinite cyclic class group On the arithmetic of Krull monoids with infinite cyclic class group

2009-08-28

arxiv.org/abs/0908.4191v1

Mathematics

Commutative Algebra

Scientific paper

Let $H$ be a Krull monoid with infinite cyclic class group $G$ and let $G_P \subset G$ denote the set of classes containing prime divisors. We study under which conditions on $G_P$ some of the main finiteness properties of factorization theory--such as local tameness, the finiteness and rationality of the elasticity, the structure theorem for sets of lengths, the finiteness of the catenary degree, and the existence of monotone and of near monotone chains of factorizations--hold in $H$. In many cases, we derive explicit characterizations.

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