Abstract

In this paper, we introduce a new generalization of coherent rings using the Gorenstein projective dimension. Let $n$ be a positive integer or $n = \infty$. A ring $R$ is called a left $G_n$-coherent ring in case every finitely generated submodule of finitely generated free left $R$-modules whose Gorenstein projective dimension ${}\leq n-1$ is finitely presented. We characterize $G_n$-coherent rings in various ways, using $G_n$-flat, $G_n$-injective modules and cotorsion theory.

Keywords: Gorenstein projective dimension, coherent, cotorsion theory.

MSC: 16E99

Pages:  155$-$163     

Volume  60 ,  Issue  3 ,  2008