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.
基金
浙江省教委科研基金资助课题!(990271)