| A Note on FP-Injective Dimension |
| Received:May 12, 2009 Revised:January 18, 2010 |
| Key Words:
generalized Gorenstein dimension $FP$-injective dimension left orthogonal dimension.
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| Fund Project:Supported by the Ph. D. Program Foundation of Ministry of Education of China (Grant No.200803570003). |
| Author Name | Affiliation | | Yang SONG | School of Mathematical Science, Anhui University, Anhui 230039, P. R. China
School of Mathematics and Statistics, Suzhou University, Anhui 234000, P. R. China | | Xian Neng DU | School of Mathematical Science, Anhui University, Anhui 230039, P. R. China | | Zhi Bing ZHAO | 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. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2011.03.010 |
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