Generalized Sets of Lengths |
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| Authors: | Scott T Chapman William W Smith |
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| Affiliation: | aTrinity University, Department of Mathematics, 715 Stadium Drive, San Antonio, Texas, 78212-7200;bThe University of North Carolina at Chapel Hill, Department of Mathematics, Chapel Hill, North Carolina, 27599-3250 |
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| Abstract: | LetRbe a Dedekind domain and (R) the set of irreducible elements ofR. In this paper, we study the sets R(n) = {m | α1,…,αn, β1,…,βm (R) such that α1,…,αn = β1,…,βm}, wherenis a positive integer. We show, in constrast to indications in some earlier work, that the sets R(n) are not completely determined by the Davenport constant of the class group ofR. We offer some specific constructions for Dedekind domains with small class groups, and show how these sets are generalizations of the sets studied earlier by Geroldinger [[9], [10]]. |
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| Keywords: | Dedekind domain block monoid zero-sum sequence factorizations |
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