On the arithmetic of Krull monoids with infinite cyclic class group


Let H be a Krull monoid with infinite cyclic class group G and let GPcG denote the set of classes containing prime divisors. We study under which conditions on GP 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 near monotone chains of factorizations-hold in H. In many cases, we derive explicit characterizations. © 2010 Elsevier B.V.

Publication Title

Journal of Pure and Applied Algebra