On Gorenstein global and
Gorenstein weak global dimensions

Junpeng Wang; Gang Yang; Qingyu Shao; Xiaoxiang Zhang

doi:10.4064/cm9052-7-2023

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On Gorenstein global and Gorenstein weak global dimensions

Volume 174 / 2023

Junpeng Wang, Gang Yang, Qingyu Shao, Xiaoxiang Zhang Colloquium Mathematicum 174 (2023), 45-67 MSC: Primary 18G25; Secondary 16E65, 18G20. DOI: 10.4064/cm9052-7-2023 Published online: 28 September 2023

Abstract

It is well-known that the weak global dimension of a ring does not exceed its global dimension. Christensen et al. obtained a corresponding result in Gorenstein setting for coherent rings. We extend this result to an arbitrary ring. As applications, we characterize the finiteness of (Gorenstein) global dimension by singularity categories and Gorenstein flat modules.

Authors

Junpeng WangDepartment of Mathematics
Northwest Normal University
Lanzhou 730070, P.R. China
e-mail
Gang YangDepartment of Mathematics
Lanzhou Jiaotong University
Lanzhou 730070, P.R. China
e-mail
Qingyu ShaoSchool of Mathematics
Southeast University
Nanjing 210096, P.R. China
e-mail
Xiaoxiang ZhangSchool of Mathematics
Southeast University
Nanjing 210096, P.R. China
e-mail

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