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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2018; 55(6): 1389-1421

Online first article June 5, 2018      Printed November 1, 2018

https://doi.org/10.4134/JKMS.j170718

Copyright © The Korean Mathematical Society.

Gorenstein weak injective modules with respect to a semidualizing bimodule

Zenghui Gao, Xin Ma, Tiwei Zhao

Chengdu University of Information Technology, Henan University of Engineering, Qufu Normal University

Abstract

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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

MSC numbers: Primary 18G05, 16E30, 18G20

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