On co-Gorenstein modules, minimal flat resolutions and dual Bass numbers
Volume 138 / 2015
Colloquium Mathematicum 138 (2015), 217-231
MSC: 13C14, 13C15, 13D07, 13E05, 13E10, 13Hxx.
DOI: 10.4064/cm138-2-6
Abstract
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.
