Purity over Prufer v-multiplication domains

It is well known that a domain R is a Prufer domain if and only if for R-modules, relative divisibility implies purity. In this paper, we extend this result to Prufer v-multiplication domains (PvMDs). To do this, we introduce the concept of w-pure exact. sequences over commutative rings with zero divisors, and we prove that a domain R is a PvMD if and only if for R-modules, relative divisibility implies w-purity. Also, we compare w-purity with purity and relative divisibility by giving examples.