Generalized coherent rings by Gorenstein projective dimension

Linlin Li, Jiaqun Wei

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.