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HOMOLOGICAL PROPERTIES OF MODULES OVER DING-CHEN RINGS

  • Yang, Gang
  • Received : 2010.07.22
  • Published : 2012.01.01

Abstract

The so-called Ding-Chen ring is an n-FC ring which is both left and right coherent, and has both left and right self FP-injective dimensions at most n for some non-negative integer n. In this paper, we investigate the classes of the so-called Ding projective, Ding injective and Gorenstein at modules and show that some homological properties of modules over Gorenstein rings can be generalized to the modules over Ding-Chen rings. We first consider Gorenstein at and Ding injective dimensions of modules together with Ding injective precovers. We then discuss balance of functors Hom and tensor.

Keywords

Ding-Chen ring;Ding projective and Ding injective module;Gorenstein flat module;precover;preenvelope;balanced functors

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Cited by

  1. Relative left derived functors of tensor product functors vol.32, pp.7, 2016, https://doi.org/10.1007/s10114-016-5245-5
  2. Singularity categories with respect to Ding projective modules vol.33, pp.6, 2017, https://doi.org/10.1007/s10114-017-6209-0
  3. On Ding homological dimensions vol.30, pp.4, 2015, https://doi.org/10.1007/s11766-015-3376-6
  4. DERIVED CATEGORIES WITH RESPECT TO DING MODULES vol.12, pp.06, 2013, https://doi.org/10.1142/S0219498813500217
  5. RELATIVE AND TATE COHOMOLOGY OF DING MODULES AND COMPLEXES vol.52, pp.4, 2015, https://doi.org/10.4134/JKMS.2015.52.4.821
  6. On Right Orthogonal Classes and Cohomology Over Ding–Chen Rings vol.40, pp.2, 2017, https://doi.org/10.1007/s40840-017-0461-4

Acknowledgement

Supported by : NSF of China