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 e...

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Bibliographic Details
Published in:Journal of pure and applied algebra 2010-08, Vol.214 (8), p.1334-1339
Main Authors: Baginski, Paul, Chapman, S.T., Rodriguez, Ryan, Schaeffer, George J., She, Yiwei
Format: Article
Language:English
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Summary: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 .
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2009.10.015