| Excellent 扩张环上Gorenstein投射模的性质 |
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| 引用本文： | 宿维军.Excellent 扩张环上Gorenstein投射模的性质[J].甘肃联合大学学报(自然科学版),2007,21(4):15-17. |
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| 作者姓名： | 宿维军 |
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| 作者单位： | 西北师范大学,数学与信息科学学院,甘肃,兰州,730070;合作民族师范高等专科学校,数学系,甘肃,合作,747000 |
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| 摘 要： | 环论主要讨论其结构及分类,近年来特别对Gorenstein环的结构与分类以及维数不变量的研究很多,本文在Excellent扩张环上对Gorenstein投射模在两个环上的性质进行了比较.给出结论:若环S是环R的Excellent扩张,则模sM是G-Proj(Gorenstein投射模)的充要条件是sM是G-Proj,且模M作为S模和M模其Gorenstein投射维数相等,即GpdsM=GpdRM.
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| 关 键 词： | Gorenstein投射模 投射维数 Excellent扩张 |
| 文章编号： | 1672-691X（2007）04-0015-03 |
| 修稿时间： | 2007-02-27 |
Properties of Gorenstein Project Modules on Excellent Extension Ring |
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| SU Wei-jun.Properties of Gorenstein Project Modules on Excellent Extension Ring[J].Journal of Gansu Lianhe University :Natural Sciences,2007,21(4):15-17. |
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| Authors: | SU Wei-jun |
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| Institution: | 1. School of Mathematics and Information Science, Northwest Normal University, Lanzhou 730070,China; 2. Department of Mathematics, Hezuo Normal College for Minorities, Hezuo 747000,China |
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| Abstract: | Ring theory discuss mainly the constructer and classify of rings,recently in particular had discussed many on Gorenstein ring and it's dimension variant.In this paper,author discussed two properties of Gorenstein projective modules on Excellent extension rings and have results:If ring S is Excellent extension of ring R,S-module SM is Gorenstein projective module if and only if R-module RM is Gorenstein projective module,more over,S-module SM and R-module RM has the same Gorenstein projective dimension,i.e.,GpdSM=GpdRM. |
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| Keywords: | Gorenstein project module project dimension excellent extension |
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