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GORENSTEIN WEAK INJECTIVE MODULES WITH RESPECT TO A SEMIDUALIZING BIMODULE

  • Gao, Zenghui (College of Applied Mathematics Chengdu University of Information Technology) ;
  • Ma, Xin (College of Science Henan University of Engineering) ;
  • Zhao, Tiwei (School of Mathematical Sciences Qufu Normal University)
  • Received : 2017.11.08
  • Accepted : 2018.03.08
  • Published : 2018.11.01

Abstract

In this paper, we introduce the notion of C-Gorenstein weak injective modules with respect to a semidualizing bimodule $_SC_R$, where R and S are arbitrary associative rings. We show that an iteration of the procedure used to define $G_C$-weak injective modules yields exactly the $G_C$-weak injective modules, and then give the Foxby equivalence in this setting analogous to that of C-Gorenstein injective modules over commutative Noetherian rings. Finally, some applications are given, including weak co-Auslander-Buchweitz context, model structure and dual pair induced by $G_C$-weak injective modules.

Acknowledgement

Supported by : NSFC, Science and Technology Foundation of Sichuan Province, Nanjing University

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