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On co-Gorenstein modules, minimal flat resolutions and dual Bass numbers

Volume 138 / 2015

Zahra Heidarian, Hossein Zakeri Colloquium Mathematicum 138 (2015), 217-231 MSC: 13C14, 13C15, 13D07, 13E05, 13E10, 13Hxx. DOI: 10.4064/cm138-2-6


The dual of a Gorenstein module is called a co-Gorenstein module, defined by Lingguang Li. In this paper, we prove that if $R$ is a local $U$-ring and $M$ is an Artinian $R$-module, then $M$ is a co-Gorenstein $R$-module if and only if the complex ${\rm Hom}_{\hat{R}}(\mathcal{C}(\mathcal{U},\hat{R}),M)$ is a minimal flat resolution for $M$ when we choose a suitable triangular subset $\mathcal{U}$ on $\hat{R}$. Moreover we characterize the co-Gorenstein modules over a local $U$-ring and Cohen–Macaulay local $U$-ring.


  • Zahra HeidarianDepartment of Mathematics
    Sciences and Research Branch
    Islamic Azad University
    Tehran, Iran
  • Hossein ZakeriDepartment of Mathematics
    Faculty of Mathematical Sciences and Computer
    Kharazmi University
    Tehran, Iran

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