陈淼森.左连续环中若干链条件的等价性[J].数学研究及应用,2001,21(2):264~266
左连续环中若干链条件的等价性
Equivalence of Some Conditions in Left Continuous Rings
投稿时间:1998-09-28  
DOI:10.3770/j.issn:1000-341X.2001.02.019
中文关键词:  左连续环  左自内射环  左Z1-环.
英文关键词:left continuous ring  left self-injective ring  left Z1-ring.
基金项目:浙江省教委科研基金资助课题(990271)
作者单位
陈淼森 浙江师范大学数学系浙江金华 321004 
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中文摘要:
      (1)设R是左连续环,则R是左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.
英文摘要:
      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-injective ring is a QF ring.2). It is proved that for a left Z1-ring R, if M is a finitely generated R-module, then M satisfies Artin-Raes property.
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