| SF-环的内射性 |
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| 引用本文： | 李艳午,程海霞.SF-环的内射性[J].纯粹数学与应用数学,2012(1):17-24. |
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| 作者姓名： | 李艳午 程海霞 |
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| 作者单位： | 芜湖信息技术职业学院;南京大学数学系;安徽师范大学数学与计算机科学学院 |
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| 基金项目： | 2009年安徽高校省级自然科学研究项目(KJ2009B017Z);安徽省教育厅优秀青年人才基金(2009SQRZ223);安徽省2008年高等学校省级教学研究重点资助项目(2008jyxm180) |
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| 摘 要： | 研究了SF-环与P-内射环的关系,构造了SF-环成为P-内射环的一系列条件.证明了SF-环R只要满足其中之一:R的每个极大左理想是有限生成的;特殊右零化子的降链条件;对R的每个极大左理想M,l(M)在R中是本质的,那么R就是P-内射环.在此基础上,利用一定条件下SF-环的P-内射性,发展了SF-环的若干新结果,这些结果部分地拓展了有关文献中的结果.
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| 关 键 词： | SF-环 正则环 P-内射环 半单环 零化子升(降)链条件 |
The injectivity of SF-Rings |
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| Li Yanwu,Cheng Haixia.The injectivity of SF-Rings[J].Pure and Applied Mathematics,2012(1):17-24. |
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| Authors: | Li Yanwu Cheng Haixia |
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| Institution: | 2,3(1.Wuhu Vocational College of Information Technology,Wuhu 241000,China;2.Department of Mathematics,Nanjing University,Nanjing 210093,China;3.College of Mathematics and Computer Science,Anhui Normal University,Wuhu 241000,China) |
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| Abstract: | In this paper,we studied the relations between the SF-rings and the P-injective rings.Firstly,we constructed some conditions that SF-rings be P-injective rings.In this section,we proved that a SF-ring R as soon as satisfies one of the conditions: every maximal left ideal of R is finitely generated and special right annihilator descending chain condition and is essential in R for any maximal left ideal of R,then R is a P-injective ring.Secondly,we developed some new results about SF-rings by their injectivity based on certain conditions.Our work extends some results of related references to some extent. |
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| Keywords: | SF-rings regular rings P-injective rings semi-simple rings annulator ACC(DCC) |
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