唯一分解整环上的局部结构

Local Structure Over Unique Factorization Domain

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.