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

Research paper by A. Geroldinger, D. J. Grynkiewicz, G. J. Schaeffer, W. A. Schmid

Indexed on: 28 Aug '09Published on: 28 Aug '09Published in: Mathematics - Commutative Algebra

#### Abstract

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.