Krull型整环的扩张与伪SM整环  

Extension of Krull type domains and Pseudo-SM domains

作　　者：杨杰[1] 罗洪[1] 李贵兵[1] 

机构地区：[1]西南民族大学计算机科学与技术学院,四川成都610041

出　　处：《西南民族大学学报（自然科学版）》2006年第5期874-877,共4页Journal of Southwest Minzu University(Natural Science Edition)

摘　　要：设R是有单位元的整环.本文刻画了Prüfer整环的扩环与Krull型整环的关系,以及R在L中的整闭包R Lc有PIT的等价条件,寻求到R Lw是Krull型整环的条件.另外,本文类比SM整环,定义了伪SM整环,研究了Krull型整环,H整环,伪SM整环与Krull整环的关系.给出了一个整环R是伪SM整环,不是SM整环的例子.证明了R是Krull型整环,又是伪SM整环,那么R是H整环;证明了R是Krull型整环,又是伪SM整环,w-dim(R)=1,那么R是Krull整环;以及证明了Krull型整环R既是TL整环,又是伪SM整环,则Rwg=K.In this paper,we characterize Krull type domains by using general star operations.We characterize the relationship between the overring of Prüfer domins and Krull type domains.We obtain the equivalent condition that the integral closure R Lc has PIT property if and only if w-dim(R)=1.We find out the condition that the w-integral closure R wL is a Krull type domain.Moreover,we define Pseudo-SM domain.We prove that R is a Krull type domain and a Pseudo-SM domain with w-dim(R)=1,then R is a Krull domain.We also obtain that a Krull type domain R is a TL domain and Pseudo-SM domain,then Rwg = K.

关 键 词：Krull整环 Krull型整环 伪SM整环 w-整环 

分 类 号：O154[理学—数学]