Gorenstein global dimensions relative to balanced pairs

Haiyu Liu, ,Department of Mathematics, Nanjing University, Nanjing 210093, China, Rongmin Zhu, Yuxian Geng, ,School of Mathematics and Physics, Jiangsu University of Technology, Changzhou 213001, China
2020 Electronic Research Archive  
Let G(X ) and G(Y) be Gorenstein subcategories induced by an admissible balanced pair (X , Y) in an abelian category A. In this paper, we establish Gorenstein homological dimensions in terms of these two subcategories and investigate the Gorenstein global dimensions of A induced by the balanced pair (X , Y). As a consequence, we give some new characterizations of pure global dimensions and Gorenstein global dimensions of a ring R.
doi:10.3934/era.2020082 fatcat:xjbj3lu3aza3joznowolsunkbe