| QF的刻划 |
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| 引用本文： | 董珺,魏杰. QF的刻划[J]. 兰州工业高等专科学校学报, 2007, 14(3): 1-3 |
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| 作者姓名： | 董珺 魏杰 |
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| 作者单位： | 兰州工业高等专科学校,基础学科部,甘肃,兰州,730050 |
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| 基金项目： | 甘肃省教育厅科研项目(0712B-02) |
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| 摘 要： | 研究了关于右零化子满足升链和降链条件的环,即Artinian环和Noether环.设R是左P-内射环且非零补左理想在R中不小,若R满足条件(*),则R是右Artinian环.证明了R是QF环当且仅当R是满足条件(*)的左2-内射环且非零补左理想在R中不小.
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| 关 键 词： | Artinian环 Noether环 QF环 |
| 文章编号： | 1009-2269（2007）03-0001-03 |
| 修稿时间： | 2007-01-10 |
A CHARACTERIZATION OF QF RINGS |
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| DONG Jun,WEI Jie. A CHARACTERIZATION OF QF RINGS[J]. Journal of Lanzhou Higher Polytechnical College, 2007, 14(3): 1-3 |
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| Authors: | DONG Jun WEI Jie |
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| Affiliation: | The Basic Courses Department of Lanzhou Polytechnic College, Lanzhou 730050,China |
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| Abstract: | In this paper,the Artinian and Noethrian rings are studied with ascending and descending chain conditions on right ideals.Let R be a left P-injective ring so that each non-zero complement left ideal is not small,it shows that if R satisfies(*),then R is right Artinian.We also prove that R is QF if and only if R is left 2-injective with satisfying(*),and every non-zero complement left ideal is not small. |
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| Keywords: | Artinian ring Noetherian ring QF rings |
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