PVMD的理想关联与w-扩环  

The connections among the ideals of PVMDs and w-overrings

作　　者：陈幼华[1] 尹华玉[1] 

机构地区：[1]四川师范大学数学与软件科学学院,成都610068

出　　处：《黑龙江大学自然科学学报》2011年第2期162-166,171,共6页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(10971090);四川师范大学科研基金资助项目(10MSL05)

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。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.

关 键 词：PVMD w-可逆 赋值环 w-扩环 

分 类 号：O153.3[理学—数学]