Quasi-Gorenstein projective and quasi-Gorenstein injective modules

In this paper, we introduce quasi-Gorenstein projective and quasi-Gorenstein injective modules, study some of their properties and investigate their behavior with respect to short exact sequences. Also, we give homological descriptions of quasi-Gorenstein homological dimensions of modules when they are finite and in this case, we prove that quasi-Gorenstein projective precover and quasi-Gorenstein injective preenvelope exist.