| 极大本质左理想是理想的SF－环 |
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| 引用本文： | 章聚乐.极大本质左理想是理想的SF－环[J].数学进展,1994(3). |
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| 作者姓名： | 章聚乐 |
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| 作者单位： | 安徽师范大学数学系 |
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| 摘 要： | 由Ｒａｍａｍｕｒｔｈｉ和Ｍｉｎｇ的两个公开问题所推动，本文证明了如下结果：（１）如果Ｒ是ＭＥＬＴ，ＳＦ－环，那么Ｒ是正则环；（２）如果Ｒ是ＭＥＬＴ，左ＣＥ－内射，右ＳＦ－环，那么Ｒ是具有有界指数的左和右自内射正则，左和右Ｖ－环．这就给出了Ｒａｍａｍｕｒｔｈｉ和Ｍｉｎｇ两个公开问题的部分回答．
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| 关 键 词： | vonNeumann正则环 自内射环 SF－环 拟duo环 MELT环 CE－内射环 |
SF-rings Whose Maximal Essential Left Ideals are Ideals |
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| Zhang Jule.SF-rings Whose Maximal Essential Left Ideals are Ideals[J].Advances in Mathematics,1994(3). |
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| Authors: | Zhang Jule |
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| Abstract: | This work is motivated by open problems posed by Ramamurthi and Ming,and the following resuIts are provedi(1)If R is an MELT,SF-ring,then R is regular;(2)if R is an MELT,left CE-injective,right SF-ring,then R is a left and right self-injec-tive regular,left and right V-ring of bounded index. These give partial answers to some questions posed by Ramamurthi and Ming. |
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| Keywords: | r von Neumann regular ring self-injective ring SF-ring quasi-duo ring MELT ring CE-injective ring |
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