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

Abstract

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 max Δ ( M ) and c ( M ) . Our methods generalize and complement a previous result concerning the elasticity of M .