| Gorenstein正则环、奇点范畴和Ding模 |
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| 引用本文： | 汪军鹏,狄振兴.Gorenstein正则环、奇点范畴和Ding模[J].数学学报,2019,62(2):331-344. |
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| 作者姓名： | 汪军鹏 狄振兴 |
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| 作者单位： | 1. 西北师范大学经济学院 兰州 730070;
2. 西北师范大学数学与统计学院 兰州 730070 |
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| 基金项目： | 国家自然科学基金资助项目（11601433）；中国博士后自然科学基金资助项目（2106M602945XB） |
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| 摘 要： | 本文证明了任意环的整体Ding投射维数和整体Ding内射维数一致,研究了奇点范畴和相对于Ding模的稳定范畴间的关系,并刻画了Gorenstein (正则)环以及环的整体维数的有限性.
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| 关 键 词： | Gorenstein正则环 Ding投射模 奇点范畴 |
Gorenstein Regular Rings,Singularity Categories and Ding Modules |
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| Jun Peng WANG,Zhen Xing DI.Gorenstein Regular Rings,Singularity Categories and Ding Modules[J].Acta Mathematica Sinica,2019,62(2):331-344. |
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| Authors: | Jun Peng WANG Zhen Xing DI |
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| Institution: | 1. Department of Economics, Northwest Normal University, Lanzhou 730070, P. R. China;
2. Department of Mathematics, Northwest Normal University, Lanzhou 730070, P. R. China |
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| Abstract: | We prove that the global Ding projective dimension and global Ding injective dimension coincide for any ring. We investigate the relationship between singularity categories and stable categories with respect to Ding modules, and characterize Gorenstein (regular) rings and the finiteness of left global dimension of rings in terms of singularity categories and Ding modules. |
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| Keywords: | Gorenstein regular ring Ding projective module singularity category |
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