| 左连续环中若干链条件的等价性 |
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| 引用本文： | 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 |
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| 作者姓名： | 陈淼森 |
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| 作者单位： | 浙江师范大学数学系, |
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| 基金项目： | 浙江省教委科研基金资助课题(990271) |
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| 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.
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| 关 键 词： | 左连续环；左自内射环；左Z1-环. |
| 文章编号： | 1000-341X(2001)02-0264-03 |
| 收稿时间： | 1998-09-28 |
| 修稿时间： | 1998-09-28 |
Equivalence of Some Conditions in Left Continuous Rings |
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| CHEN Miao-sen. Equivalence of Some Conditions in Left Continuous Rings[J]. Journal of Mathematical Research with Applications, 2001, 21(2): 264-266 |
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| Authors: | CHEN Miao-sen |
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| Affiliation: | Zhejiang Normal University, Jinhua 312004, China |
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| Abstract: | 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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| Keywords: | left continuous ring left self-injective ring left Z1-ring. |
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