A REMARK ON HALF-FACTORIAL DOMAINS

An atomic integral domain R is a half-factorial domain (HFD) if when- ever x1 ···xm = y1 ···yn with each xi,yj 2 R irreducible, then m = n. In this paper, we show that if R(X) is an HFD, then Clt(R) � Clt(R(X)), and if G1 are torsion abelian groups, then there exists a Dedekind HFD R such that Cl(R) = G1 � G2.