| 关于FP-内射维数的一个注记 |
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| 引用本文： | 宋杨,杜先能,赵志兵.关于FP-内射维数的一个注记[J].数学研究及应用,2011,31(3):462-466. |
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| 作者姓名： | 宋杨 杜先能 赵志兵 |
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| 作者单位： | 安徽大学数学科学学院, 安徽 合肥 230039; 宿州学院数学与统计学院, 安徽 宿州 234000;安徽大学数学科学学院, 安徽 合肥 230039;安徽大学数学科学学院, 安徽 合肥 230039 |
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| 基金项目： | 教育部博士点基金资助项目(Grant No.200803570003). |
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| 摘 要： | Let R and S be a left coherent ring and a right coherent ring respectively,RωS be a faithfully balanced self-orthogonal bimodule.We give a sufficient condition to show that l.FP-idR（ω） ∞ implies G-dimω（M） ∞,where M ∈ modR.This result generalizes the result by Huang and Tang about the relationship between the FP-injective dimension and the generalized Gorenstein dimension in 2001.In addition,we get that the left orthogonal dimension is equal to the generalized Gorenstein dimension when G-dimω（M） is finite.
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| 关 键 词： | generalized Gorenstein dimension FP-injective dimension left orthogonal dimension. |
| 收稿时间： | 2009/5/12 0:00:00 |
| 修稿时间： | 2010/1/18 0:00:00 |
A Note on FP-Injective Dimension |
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| Yang SONG,Xian Neng DU and Zhi Bing ZHAO.A Note on FP-Injective Dimension[J].Journal of Mathematical Research with Applications,2011,31(3):462-466. |
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| Authors: | Yang SONG Xian Neng DU and Zhi Bing ZHAO |
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| Institution: | 1. School of Mathematical Science, Anhui University, Anhui 230039, P. R. China;School of Mathematics and Statistics, Suzhou University, Anhui 234000, P. R. China
2. School of Mathematical Science, Anhui University, Anhui 230039, P. R. China |
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| Abstract: | Let $R$ and $S$ be a left coherent ring and a right coherent ring respectively, $_R\omega_S$ be a faithfully balanced self-orthogonal bimodule. We give a sufficient condition to show that $l.FP\mbox{-}\id_R(\omega)<\infty$ implies $ G\mbox{-}\dim_{\omega}(M)<\infty$, where $M\in$ mod\,$R$. This result generalizes the result by Huang and Tang about the relationship between the FP-injective dimension and the generalized Gorenstein dimension in 2001. In addition, we get that the left orthogonal dimension is equal to the generalized Gorenstein dimension when $G\mbox{-}\dim_{\omega}(M)$ is finite. |
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| Keywords: | generalized Gorenstein dimension $FP$-injective dimension left orthogonal dimension |
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