ELASTICITY OF FACTORIZATIONS IN INTEGRAL-DOMAINS

For an atomic integral domain R, define rho(R) = sup{m/n\ x1 ... x(m) = y1 ... y(n), each x(i), y(j) is-an-element-of R is irreducible). We investigate rho(R), with emphasis for Krull domains R. When R is a Krull domain, we determine lower and upper bounds for rho(R); in particular, rho(R) less-than-or-equal-to max{\Cl(R)\/2, 1}. Moreover, we show that for any real number r greater-than-or-equal-to 1 or r = infinity, there is a Dedekind domain R with torsion class group such that rho(R) = r.