A NEW CHARACTERIZATION OF PRÜFER v-MULTIPLICATION DOMAINS

Let D be an integral domain and w be the so-called w-operation on D. In this note, we introduce the notion of *(w)-domains: D is a *(w)-domain if $(({\cap}(x_i))({\cap}(y_j)))_w={\cap}(x_iy_j)$ for all nonzero elements $x_1,{\ldots},x_m$; $y_1,{\ldots},y_n$ of D. We then show that D is a $Pr{\ddot{u}}fer$ v-multiplication domain if and only if D is a *(w)-domain and $A^{-1}$ is of finite type for all nonzero finitely generated fractional ideals A of D.