Chinese Quarterly Journal of Mathematics ›› 2017, Vol. 32 ›› Issue (3): 255-260.doi: 10.13371/j.cnki.chin.q.j.m.2017.03.004

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On Rings with Finite Global Gorenstein Dimensions

  

  1. Department of Mathematics, Northwest Normal University
  • Received:2015-12-11 Online:2017-09-30 Published:2020-10-22
  • About author:REN Wei(1983-), male, native of Longnan, Gansu, an associate professor of Northwest Normal University, Ph.D., engages in homological algebra; ZHANG Yu(1994-), female, native of Yuncheng, Shanxi, a master degree candidate of Northwest Normal University, engages in homological algebra.
  • Supported by:
    Supported by the National Natural Science Foundation of China(11401476); Supported by the Project for Universities of Gansu Province(2015A-019);

Abstract: As a proper setting to study Gorenstein projective and injective dimensions of modules via vanishing of Gorenstein Ext-functors, a notion of a generalized Gorenstein ring is introduced, which is a non-trivial generalization of Gorenstein rings. Moreover, a new proof for Bennis and Mahdou’s equality of global Gorenstein dimension is given. 

Key words: generalized Gorenstein ring, Gorenstein projective(injective) dimension

CLC Number: