Elasticity of factorizations in integral domains |
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Authors: | D D Anderson David F Anderson |
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Institution: | Department of Mathematics, The University of Iowa, Iowa City, IA 52242, USA Department of Mathematics, The University of Tennessee, Knoxville, TN 37996, USA |
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Abstract: | For an atomic integral domain R, define(R)=sup{mn|x1xm=y1yn, each xi,yjεR is irreducible}. We investigate (R), with emphasis for Krull domains R. When R is a Krull domain, we determine lower and upper bounds for (R); in particular,(R)≤max{|Cl(R)| 2, 1}. Moreover, we show that for any real numbers r≥1 or R=∞, there is a Dedekind domain R with torsion class group such that (R)=r. |
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