左连续环中若干链条件的等价性  

Equivalence of Some Conditions in Left Continuous Rings

作　　者：陈淼森[1] 

机构地区：[1]浙江师范大学数学系,浙江金华321004

出　　处：《Journal of Mathematical Research and Exposition》2001年第2期264-266,共3页数学研究与评论（英文版）

基　　金：浙江省教委科研基金资助课题!(990271)

摘　　要：（１）设Ｒ是左连续环，则Ｒ是在Ａｒｔｉｎ环当且仅当Ｒ满足左限制有限条件当且仅当Ｒ关于本质左理想满足极小条件当且仅当Ｒ关于本质左理想满足极大条件，同时给出一个左自内射环是ＱＦ环的充要条件；（２）证明了左 Ｚ１－环上的有限生成模都有 Ａｒｔｉｎ－Ｒｅｅｓ性质．In this paper, we obtain following results: 1). Let R be a left continuous ring, then R be a left Artinian iff R satisfies left restricted finite condition iff R satisfies DCC on essential left ideals iff R satisfies ACC on essential left ideals. In addition we give a sufficient and necessary condition under which a left self-injec- tive ring is a QF ring. 2). It is proved that for a left Z1-ring R, if Mis a finitely generated R-module, then M satisfies Artin-Rees property.

关 键 词：左连续环 左自内射环 左Z1-环 本质左理想 Artin-Rees性质 结合环 有限生成模 EXTENDING模 QF环 

分 类 号：O153.3[理学—数学]