Elasticity of factorizations in integral domains

AbstractFor an atomic integral domain R, defineϱ(R)=sup{m⧸n|x1⋯xm=y1⋯yn, each xi,yjϵR is irreducible}. We investigate ϱ(R), with emphasis for Krull domains R. When R is a Krull domain, we determine lower and upper bounds for ϱ(R); in particular,ϱ(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 ϱ(R)=r