Applications of n-Gorenstein projective and injective modules

作者：Tang, Xi^*

来源：Hacettepe Journal of Mathematics and Statistics, 2015, 44(6): 1435-1443.

DOI：10.15672/hjms.2015449673

• n-Gorenstein projective module
• n-Gorenstein injective module
• n-Gorenstein projective dimension
• n-Gorenstein injective dimension

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.

• 出版日期2015-12
• 单位桂林理工大学