中文摘要：

利用整环R的理想之间的关联,给出了PVMD的一些等价刻画。证明整闭整环R是PVMD当且仅当存在正整数k〉1,使得对任意A,B∈F（R）,A∩Bkw=（Ak）w∩（Bk）w。同时讨论PVMD的w-扩环及其w-素谱,证明若R是PVMD,且R的每一素理想都是某个主理想的根,则R的w-扩环必是R的分式环。

英文摘要：

Some equivalent characterizations of PVMDs are investigated by utilizing the connections among the ideals of an integral domain R.It is proved that an integrally closed domain R is a PVMD if and only if there is a positive integer k1 such that（（A∩B）k）w=（Ak）w∩（Bk）w for any A,B∈F（R）.Meanwhile,the w-overrings of a PVMD and its w-spectrum are discussed.It is shown that if R is a PVMD and each prime ideal of R is the radical of a principal ideal,then each w-overring of R is a quotient ring of R.