| 关于强Clean一般环 (英) |
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| 引用本文： | 王周,陈建龙.关于强Clean一般环 (英)[J].数学研究及应用,2007,27(1):28-34. |
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| 作者姓名： | 王周 陈建龙 |
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| 作者单位： | 东南大学数学系,江苏,南京,210096 |
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| 基金项目： | 国家自然科学基金;江苏省自然科学基金 |
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| 摘 要： | 本文介绍了强clean—般环的概念并将一些基本的结果推广到这个更广的环类．证明了强clean一般环的角落环和强π-正则一般环都是强clean的,还讨论了强clean一般环的扩张并且证明了满足条件J(I)=Q(I)的交换clean一般环的上三角矩阵环是强clean的．
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| 关 键 词： | 强clean一般环 强π-正则一般环 上三角矩阵环 strongly π-regular general ring |
| 文章编号： | 1000-341X(2007)01-0028-07 |
| 收稿时间： | 2005/11/18 0:00:00 |
| 修稿时间： | 7/3/2006 12:00:00 AM |
On Strongly Clean General Rings |
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| WANG Zhou and CHEN Jian-long.On Strongly Clean General Rings[J].Journal of Mathematical Research with Applications,2007,27(1):28-34. |
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| Authors: | WANG Zhou and CHEN Jian-long |
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| Institution: | Department of Mathematics, Southeast University, Jiangsu 210096, China;Department of Mathematics, Southeast University, Jiangsu 210096, China |
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| Abstract: | In this paper, we introduce the concept of strongly clean general ring (with or without unity) and extend some of the basic results to a wider class. We prove that every strongly $\pi$-regular general ring is strongly clean and the corner of the strongly clean general ring is strongly clean. It is also proved that upper triangular matrix rings of the commutative clean general ring with $J(I)=Q(I)$ are strongly clean. |
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| Keywords: | strongly clean general ring upper triangular matrix ring |
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