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

Zahra Heidarian¹ ; Hossein Zakeri²

¹ Department of Mathematics Sciences and Research Branch Islamic Azad University Tehran, Iran
² Department of Mathematics Faculty of Mathematical Sciences and Computer Kharazmi University Tehran, Iran

Colloquium Mathematicum, Tome 138 (2015) no. 2, pp. 217-231

Résumé

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.

Détail

DOI : 10.4064/cm138-2-6

Keywords: dual gorenstein module called co gorenstein module defined lingguang paper prove local u ring artinian r module co gorenstein r module only complex hom hat mathcal mathcal hat minimal flat resolution choose suitable triangular subset mathcal hat moreover characterize co gorenstein modules local u ring cohen macaulay local u ring