Weak Gorenstein Graded Modules

Let R be a graded ring. The concepts of weak Gorenstein gr-projective modules, gr-injective modules and gr-flat modules are introduced, and some homological characterizations of weak Gorenstein gr-projective modules are given. It is shown that a weak Gorenstein gr-projective module is a Gorenstein gr-projective R-module over a graded n-Gorenstein ring R. Moreover, it is proved that: if any graded injective R-module has a finite graded flat dimension, then a graded module M is weak Gorenstein gr-flat if and only if M is Gorenstein gr-flat.