曹天涯,刘仲奎,杨晓燕.Gorenstein AC亏范畴*[J].数学年刊A辑,2022,43(2):213~226
Gorenstein AC亏范畴*
The Gorenstein AC Defect Category
Received:January 12, 2020  Revised:August 18, 2021
DOI:10.16205/j.cnki.cama.2022.0014
中文关键词:  Gorenstein AC 导出范畴, Gorenstein AC 亏范畴, Gorenstein AC奇点范畴, 稳定范畴
英文关键词:Gorenstein AC derived category, Gorenstein AC singularity category, Gorenstein AC defect category, Stable category
基金项目:甘肃省自然科学基金(No.21JR1RA229)和甘肃省高等学校创新基金(No.2020A-11)
Author NameAffiliation
CAO Tianya College of Computer Science and Engineering, Northwest Normal University,Lanzhou 730070, China. 
LIU Zhongkui College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China. 
YANG Xiaoyan College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China. 
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中文摘要:
      作者定义了Gorenstein AC导出范畴 Dbgac(R)并且和导出范畴作了一些比较.作者定义了Gorenstein AC奇点范畴 Dbgacsg(R),在这个范畴中具有有限Gorenstein AC- 投射维数的模都是零对象.同时, 作者给出了由Gorenstein AC- 投射模构成的稳定范畴到奇点范畴的三角嵌入 F : GAC → Dbsg(R) .通过作函子 F 的商引入Gorenstein AC亏范畴 Dbgacd(R),并且给出三角等价 Dbgacd(R) = Dbgacsg(R)
英文摘要:
      The authors introduce the Gorenstein AC derived category Dbgac(R) and compare it with the derived category. Then the Gorenstein AC singularity category Dbgacsg(R) is defined since its vanishing implies the finiteness of the Gorenstein AC-projective resolution dimension of any R-module. They give a triangle-embedding functor F : GAC → Dbsg(R),from the stable category of Gorenstein AC-projective modules to the bounded singular category. the Gorenstein AC defect category Dbgacd(R) is defined as the quotient of F.Moreover, it is proved that Dbgacd(R) is triangle-equivalent to Dbgacsg(R).
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