| 摘要: |
| 本文研究了Gorenstein投射维数的相关问题.利用经典同调维数的研究方法,给出了Gorenstein投射维数有限模的Gorenstein投射维数的一个刻画,并利用这一结果证明了Gorenstein完全环和Artin环的Gorenstein整体维数分别由各自的循环模和单模的Gorenstein投射维数来确定.这些结论丰富了Gorenstein同调代数理论. |
| 关键词: Gorenstein 投射模 Gorenstein 投射维数 Gorenstein 整体维数 |
| DOI： |
| 分类号:O154.2 |
| 基金项目:国家自然科学青年基金(11401001)安徽省高校优秀人才基金(2013SQRL071ZD);安徽大学博士启动基金(33190141). |
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| A NOTE ON GORENSTEIN PROJECTIVE DIMESION |
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ZHAO Zhi-Bing1, JIANG Ge2
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1.School of Math. Sci., Anhui University, Hefei 230601, China;2.Department of Math. and Phy., Bengbu University, Bengbu 233030, China
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| Abstract: |
| In this paper, we consider some questions related to Gorenstein projective dimension. By using the method which study the classical homological dimension, we give a sufficient condition of Gorenstein projective dimension of a module smaller than or equal to n when it is flnite. As an application, we prove that the Gorenstein global dimension of a Goresntein perfect ring or an artinian ring is completed determined by the Gorenstein projective dimensions of the cyclic modules and simple modules over it respectively, which extended the theory of Gorenstein homological algebra. |
| Key words: Gorenstein projective modules Gorenstein projective dimension Gorenstein global dimension |
