Applications of n-Gorenstein projective and injective modules

Year 2015, Volume: 44 Issue: 6, 1435 - 1443, 01.12.2015

Xi Tang

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

References

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