The Quasi-Ω-Domains With PVMD

We characterize a quasi-Ω-domains with PVMD.And we prove that if R is a quasi-Ω-domain with PVMD,then ω-D(ω-J(P))=ω-P^↓,or ω-D(ω-J(P))=w-P^↓Pwith P being unbranched for each nonzero prime ω-ideal P of R.And then we prove that if R is a quasi-Ω-domain with PVMD,P and N are two incomparable prime ω-ideals of R,and J=∩Q|Q∈ω-N^↓\ω-P^↓,then J is a prime w-ideal,and .