• Title/Summary/Keyword: $G_C$-weak injective module

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GORENSTEIN WEAK INJECTIVE MODULES WITH RESPECT TO A SEMIDUALIZING BIMODULE

  • Gao, Zenghui;Ma, Xin;Zhao, Tiwei
    • Journal of the Korean Mathematical Society
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    • v.55 no.6
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    • pp.1389-1421
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    • 2018
  • 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.

GORENSTEIN FPn-INJECTIVE MODULES WITH RESPECT TO A SEMIDUALIZING BIMODULE

  • Zhiqiang Cheng;Guoqiang Zhao
    • Journal of the Korean Mathematical Society
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    • v.61 no.1
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    • pp.29-40
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    • 2024
  • Let S and R be rings and SCR a semidualizing bimodule. We introduce the notion of GC-FPn-injective modules, which generalizes GC-FP-injective modules and GC-weak injective modules. The homological properties and the stability of GC-FPn-injective modules are investigated. When S is a left n-coherent ring, several nice properties and new Foxby equivalences relative to GC-FPn-injective modules are given.