Almost splitting sets in integral domains, II

Let D be an integral domain. A saturated multiplicative subset S of D is an almost splitting set if, for each 0≠dset membership, variantD, there exists a positive integer n=n(d) such that dn=st for some sset membership, variantS and tset membership, variantD which is v-coprime to each element of S. We show that every upper to zero in D[X] contains a primary element if and only if Dset minus{0} is an almost splitting set in D[X], if and only if D is a UMT-domain and Cl(D[X]) is torsion. We also prove that D[X] is an almost GCD-domain if and only if D is an almost GCD-domain and Cl(D[X]) is torsion. Using this result, we construct an integral domain D such that Cl(D) is torsion, but Cl(D[X]) is not torsion.