理想链条件与诣零理想链条件  

IDEAL CHAIN CONDITION AND NILIDEAL CHAIN CONDITION

作　　者：朱庚申[1] 张友[2] 张敏[2] 

机构地区：[1]中国环境管理干部学院 [2]四平师范学院

出　　处：《松辽学刊（自然科学版）》1993年第3期19-22,共4页Songliao Journal (Natural Science Edition)

摘　　要：本文讨论了环R的诣零右理想链条件包含右理想链条件的充分必要条件,进一步给出了环R的右理想极小条件包含右理想极大条件的充分必要条件是R的诣零右理想满足极大条件,从而使Hopking定理成为本文定理3的推论。In this paper,R denotes an associative ring. N the koethe radical of R. We defined certain property of R and studied the relations between the rings which satisfies the chain condition for ideal and nilideal. We obtain the main results in this paper theorem 3: An Artiniar ring R is Noetherian Ring if and only if R satisfies ascending chain condition for one-side nilideal.

关 键 词：链条件 理想 诣零理想 环 阿丁环 

分 类 号：O153.3[理学—数学]