Applications of n-Gorenstein projective and injective modules
Over a commutative noetherian ring, we introduce a generalization of
Gorenstein projective and injective modules, which we call, respectively,
n-Gorenstein projective and injective modules. These last two classes
of modules give us a new characterization of Gorenstein rings in terms
of top local cohomology modules of flat modules. We also utilize the
n-Gorenstein injective dimension to study an open question of Takahashi. Furthermore, we prove that a nonzero finite module with finite
n-Gorenstein projective dimension satisfies the Auslander-Bridger formula.