Generalized coherent rings by Gorenstein projective dimension

Abstract

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