Applications of n-Gorenstein projective and injective modules

Authors : Xi TANG

Pages : 1435-1443

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Publication Date : 2015-12-01

Article Type : Research Paper

Abstract :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. 
Keywords : n Gorenstein projective module, n Gorenstein injective module, n Gorenstein projective dimension, n Gorenstein injective dimension