a b s t r a c t 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 ∆(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 ∆(M) and c(M). Our methods generalize and complement a previous result concerning the elasticity of M.
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