DOI QR코드

DOI QR Code

RELATIVE AND TATE COHOMOLOGY OF DING MODULES AND COMPLEXES

  • ZHANG, CHUNXIA (Department of Mathematics Northwest Normal University)
  • Received : 2014.10.04
  • Published : 2015.06.01

Abstract

We investigate the relative and Tate cohomology theories with respect to Ding modules and complexes, consider their relations with classical and Gorenstein cohomology theories. As an application, the Avramov-Martsinkovsky type exact sequence of Ding modules is obtained.

Keywords

Acknowledgement

Supported by : National Natural Science Foundation of China

References

  1. L. L. Avramov and H.-B. Foxby, Homological dimension of unbounded complexes, J. Pure Appl. Algebra 71 (1991), no. 2-3, 129-155. https://doi.org/10.1016/0022-4049(91)90144-Q
  2. L. L. Avramov and A. Martsinkovsky, Absolute, relative, and Tate cohomology of modules of finite Gorenstein dimension, Proc. London Math. Soc. 85 (2002), no. 2, 393-440. https://doi.org/10.1112/S0024611502013527
  3. N. Q. Ding, Y. L. Li, and L. X. Mao, Strongly Gorenstein flat modules, J. Aust. Math. Soc. 86 (2009), no. 3, 323-338. https://doi.org/10.1017/S1446788708000761
  4. E. E. Enochs and O. M. G. Jenda, Resolutions by Gorenstein injective and projective modules and modules of finite injective dimension over Gorenstein rings, Comm. Algebra 23 (1995), no. 3, 869-877. https://doi.org/10.1080/00927879508825254
  5. E. E. Enochs and O. M. G. Jenda, Relative homological algebra, De Gruyter Expositions in Mathematics no. 30, Walter De Gruyter, New York, 2000.
  6. J. Gillespie, Model structures on modules over Ding-Chen rings, Homology Homotopy Appl. 12 (2010), no. 1, 61-73. https://doi.org/10.4310/HHA.2010.v12.n1.a6
  7. R. Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics 52, Springer-Verlag, New York-Heidelberg, 1977.
  8. H. Holm, Gorenstein derived functors, Proc. Amer. Math. Soc. 132 (2004), no. 7, 1913-1923. https://doi.org/10.1090/S0002-9939-04-07317-4
  9. A. Iacob, Generalized Tate cohomology, Tsukuba J. Math. 29 (2005), no. 2, 389-404. https://doi.org/10.21099/tkbjm/1496164963
  10. N. Mahdou and M. Tamekkante, Strongly Gorenstein flat modules and dimensions, Chin. Ann. Math. Ser. B 32 (2011), no. 4, 533-548. https://doi.org/10.1007/s11401-011-0659-y
  11. L. X. Mao and N. Q. Ding, Gorenstein FP-injective and Gorenstein flat modules, J. Algebra Appl. 7 (2008), no. 4, 491-506. https://doi.org/10.1142/S0219498808002953
  12. K. Pinzon, Absolutely pure covers, Comm. Algebra 36 (2008), 2186-2194. https://doi.org/10.1080/00927870801952694
  13. W. Ren, Z. K. Liu, and G. Yang, Derived categories with respect to Ding modules, J. Algebra Appl. 12 (2013), no. 6, 1350021, 14 pp.
  14. O. Veliche, Gorenstein projective dimension for complexes, Trans. Amer. Math. Soc. 358 (2006), no. 3, 1257-1283. https://doi.org/10.1090/S0002-9947-05-03771-2
  15. Z. P. Wang, Reseaches of relative homological properties in the category of complexes, Ph.D. thesis, Northwest Normal University, China, 2010.
  16. C. H. Yang, Strongly Gorenstein flat and Gorenstein FP-injective modules, Turkish J. Math. 37 (2013), no. 2, 218-230.
  17. G. Yang, Homological properties of modules over Ding-Chen rings, J. Korean Math. Soc. 49 (2012), no. 1, 31-47. https://doi.org/10.4134/JKMS.2012.49.1.031
  18. G. Yang, Z. K. Liu, and L. Liang, Ding projective and Ding injective modules, Algebra Colloq. 20 (2013), no. 4, 601-612. https://doi.org/10.1142/S1005386713000576

Cited by

  1. Avramov–Martsinkovsky type exact sequences with tor functors 2017, https://doi.org/10.1007/s10114-017-7089-z