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http://dx.doi.org/10.4134/JKMS.j170718

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)
Publication Information
Journal of the Korean Mathematical Society / v.55, no.6, 2018 , pp. 1389-1421 More about this Journal
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.
Keywords
(faithfully) semidualizing bimodule; C-weak injective module; $G_C$-weak injective module; Foxby equivalence; weak co-Auslander-Buchweitz context; dual pair;
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Times Cited By KSCI : 1  (Citation Analysis)
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