| 关于极大内射性的注记 |
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| 引用本文： | 赵国,汪明义.关于极大内射性的注记[J].四川大学学报(自然科学版),2005,42(5):859-866. |
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| 作者姓名： | 赵国 汪明义 |
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| 作者单位： | 1. 西南民族大学计算机科学与技术学院,成都,610041
2. 四川师范大学数学研究所,成都,610068 |
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| 基金项目： | Fundation item四川省教育厅重点科研基金;四川省青年科学基金;Acknowledgement It is a great pleasure for the first author to thank heartily his colleague Luo Rong for his valuable suggestions and discussions. |
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| 摘 要： | 环R上的右R-模E称为极大内射模，如果对每个极大右理想m，任何右R-模同态f：m→E都能扩张成右R-模同态f′：R→E．在本文中，作者应用极大内射模和函子Ext将内射维数推广到极大内射维数，并证明其为单模的投射维数的上确界、然后详细地考察了其特征模为极大内射模的一类模，揭示了这类模与关于Von Neumann正则环的Ramamurthi问题的内在联系，给出了关于Ramamurthi问题的部分结果．
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| 关 键 词： | 自内射环 平坦模 Von Neumann正则环 |
| 文章编号： | 0490-6756（2005）05-0859-08 |
| 收稿时间： | 2003-12-18 |
| 修稿时间： | 2003-12-182004-02-24 |
Some Notes on Maximal Injectivity |
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| ZHAO Guo,WANG Ming-yi.Some Notes on Maximal Injectivity[J].Journal of Sichuan University (Natural Science Edition),2005,42(5):859-866. |
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| Authors: | ZHAO Guo WANG Ming-yi |
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| Abstract: | A right R-module E over a ring R is said to be maximally injective in case for any maxi-mal right ideal m of R , every R-homomorphism f: m → E can be extended to a R-homomor-phism f': R → E . In this paper, the authors first extend the conception of injective dimensionsof any ring R to that of maximally injective dimensions, which turns out to be precisely the supre-mum of projective dimensions of simple R-modules. Then they investigate modules with maximal-ly injective character modules, which has inherent connection with an famous open problem of Ra-mamurthi concerning Von Neumann regular rings. They end this paper with a partial affirmativeanswer to Ramamurthi's problem under the right socular assumption. |
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| Keywords: | self-injective rings flat modules Von Neumann regular rings |
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