| 有限生成亚投射模范畴 |
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| 引用本文： | 冯良贵,郝志峰.有限生成亚投射模范畴[J].数学研究及应用,2002,22(2):215-218. |
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| 作者姓名： | 冯良贵 郝志峰 |
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| 作者单位： | 1. 国防科技大学数学与系统科学系,湖南长沙410073
2. 华南理工大学应用数学系,广东,广州,510641,中科院软件所,北京,100080 |
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| 基金项目： | Supported by the National Natural Science Foundation of China(1990100),theNatural Science Foundation of Guangdong Province. |
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| 摘 要： | 对一个QF环R,本文证明:其投射左R模范畴是因式分解范畴当且仅当gl.dim R≤1．进一步,若 P(RR)＝P(RR)＝0,则其通过左模而得到的亚 Crothendieck群与其通过右模而得到的亚Grothendieck群在同构意义下是一样的．还证明了有限生成亚投射左R－模范畴不仅是一个因式分解范畴而且是一个带积的具有小的骨架子范畴的范畴．
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| 关 键 词： | 有限生成 亚投射 模范畴 QF环 亚Grothenchieck群 同构 |
| 收稿时间： | 1999/3/22 0:00:00 |
The Category of Finitely Generated Meta-ProjectiveLeft R-Modules |
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| FENG Liang-gui and HAO Zhi-feng.The Category of Finitely Generated Meta-ProjectiveLeft R-Modules[J].Journal of Mathematical Research with Applications,2002,22(2):215-218. |
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| Authors: | FENG Liang-gui and HAO Zhi-feng |
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| Institution: | Dept. of Sys. Eng. & Math.; National Univ. of Defence Tech.; Changsha; China;Dept. of Appl. Math.; South China University of Technology; Guangzhou; Inst. of Software; Chinese Academy of Sciences; Beijing 100080, China |
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| Abstract: | In this paper,it is shown that for a QF ring R, the category of projective left R-modules is a category with factorization if and only if gl.dimR _< 1,moreover, if P(RR) = P(RR) = 0,then the meta-Grothendieck groups obtained by left modules or by right modules are the same,up to isomorphism. It is also shown that the category of f.g. meta-pojective left R-modules is not only a category with factorization but also a category with product such that it has a small skeletal subcategory. |
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| Keywords: | meta-projective module meta-Grothendieck group category with factor-ization |
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