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Gorenstein正则环、奇点范畴和Ding模
Gorenstein Regular Rings, Singularity Categories and Ding Modules
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.
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.
Gorenstein 正则环 / Ding 投射模 / 奇点范畴 {{custom_keyword}} /
Gorenstein regular ring / Ding projective module / singularity category {{custom_keyword}} /
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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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