| 正则环的投射根 |
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| 引用本文： | 卢丹诚,佟文廷. 正则环的投射根[J]. 数学研究及应用, 2004, 24(4): 603-609 |
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| 作者姓名： | 卢丹诚 佟文廷 |
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| 作者单位： | 1. 苏州大学数学系,江苏,苏州,215006
2. 南京大学数学系,江苏,南京,210093 |
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| 基金项目： | SupportedbyNationalNaturalScienceFoundofChina(10071035) |
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| 摘 要： | 研究了正则环上投射根的性质.证明了正则环的投射根左右对称,且模去投射根的正则环只有零投射根.给出了矩阵环及角落环投射根的计算式,并得到了投射根为零的正则环的一些刻画。最后讨论了投射根为零的正则环在各种环运算下的封闭性和正则环的MP-维数.
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| 关 键 词： | 投射根 底座 正则环 MP-维数 |
| 收稿时间： | 2003-01-10 |
On the Projective Radicals of Regular Rings |
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| LU Dan-cheng and TONG Wen-ting. On the Projective Radicals of Regular Rings[J]. Journal of Mathematical Research with Applications, 2004, 24(4): 603-609 |
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| Authors: | LU Dan-cheng and TONG Wen-ting |
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| Affiliation: | Dept. of Math.; Suzhou University; Jiangsu; China;Dept. of Math.; Nanjing University; China |
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| Abstract: | We study the properties of projective radicals of regular rings. It is shown that the projective radical of a regular ring is left-right symmetric and a regular ring modulo its projective radical has zero projective radical. Also, we obtain a relation between projective radicals of a finitely generated projective module over a regular ring and its endomorphism ring, from which we give formulas about projective radicals of matrix rings and corners of a regular ring, and some equivalent conditions for a regular ring with zero projective radicals are given. |
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| Keywords: | projective radical socle regular rings MP-dimension |
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