Artin 环与 Noether 环  

Artin Ring and Noetherian Ring

作　　者：杨晓莹 张友[2] 

机构地区：[1]长春水利电力高等专科学校 [2]东北大学秦皇岛分校

出　　处：《吉林工学院学报（自然科学版）》1998年第2期77-80,共4页Journal of Jilin Institute of Technology

摘　　要：通过讨论满足理想链条件和诣零理想链条件的环之间的关系。得到了Ａｒｔｉｎ环成为Ｎｏｅｔｈｅｒ环的等价条件。其结果如下：（１）设Ｒ为结合环，则Ｒ的右理想极小条件包含右理想极大条件Ｒ的诣零右理想满足极大条件。（２）设Ｒ为非幂零的结合环，则Ｒ的右理想极小条件包含右理想极大条件存在主幂等元ｅ，使ｅ在Ｒ中的右零化子ｒ（ｅ）具备右理想极大条件。Based on a study on the relationship between rings which satisfies the ideal and nilideal chain conditions, the equivalent condition for an Artin ring to be a Noetherian ring is obtained. The results are as follows:① An Artin ring R is a Noetherian ring if and only if R satisfies the ascending chain condition for one side nilideal;② Assuming R is the nonnilpotent Artin ring, then ring R is a Noetherian ring if and only if there exists a principal idempotence of R and the right annihilator of e in R satisfies the ascending chain condition for right ideal.

关 键 词：阿丁环 诺特尔环 结合环 理想链条件 

分 类 号：O153.3[理学—数学]