唯一分解整环上的局部结构  

Local Structure Over Unique Factorization Domain

作　　者：陈焕艮[1] 

机构地区：[1]湖南师范大学数学系

出　　处：《数学研究》1996年第2期88-90,共3页Journal of Mathematical Study

摘　　要：利用局部化环，给出了环为唯一分解整环的充要条件，推广了Ａｕｓｌａｎｄｅｒ等人的结果．In this paper,we find necessary and sufficient condition on R so that R should be a unique factorization domain. As its applications,we obtain the following results:(1)Let R be regular.Then R is a finite direct sum of unique factorization domains if and only if PicR=1.(2)Let R be coherent with w.gl.dimR>∞.Then R is a unique factorization domain if and only if R is a Krull domain with PicR=1.(3)Let R be a Krull domain with gl.dimR≤2.Then R is a unique factorization domain if and only if PicR=1.

关 键 词：唯一分解整环 正则局部环 PF环 平凡Picard群 

分 类 号：O153.3[理学—数学] O152[理学—基础数学]