On the Delta set and catenary degree of Krull monoids with infinite cyclic divisor class group

Let M be a Krull monoid with divisor class group Z, and let S⊆Z denote the set of divisor classes of M which contain prime divisors. We find conditions on S equivalent to the finiteness of both Δ(M), the Delta set of M, and c(M), the catenary degree of M. In the finite case, we obtain explicit upper bounds on maxΔ(M) and c(M). Our methods generalize and complement a previous result concerning the elasticity of M.