DOI QR코드

DOI QR Code

STRONGLY GORENSTEIN C-HOMOLOGICAL MODULES UNDER CHANGE OF RINGS

  • Liu, Yajuan (Department of Applied Mathematics Northwest Normal University) ;
  • Zhang, Cuiping (Department of Mathematics Northwest Normal University)
  • 투고 : 2020.08.09
  • 심사 : 2021.03.10
  • 발행 : 2021.07.31

초록

Some properties of strongly Gorenstein C-projective, C-injective and C-flat modules are studied, mainly considering these properties under change of rings. Specifically, the completions of rings, the localizations and the polynomial rings are considered.

키워드

과제정보

This work was supported by National Natural Science Foundation of China (No. 11761061).

참고문헌

  1. M. Auslander and M. Bridger, Stable module theory, Memoirs of the American Mathematical Society, No. 94, American Mathematical Society, Providence, RI, 1969.
  2. H. Bass, Injective dimension in Noetherian rings, Trans. Amer. Math. Soc. 102 (1962), 18-29. https://doi.org/10.2307/1993878
  3. D. Bennis and N. Mahdou, Strongly Gorenstein projective, injective, and flat modules, J. Pure Appl. Algebra 210 (2007), no. 2, 437-445. https://doi.org/10.1016/j.jpaa.2006.10.010
  4. E. E. Enochs and O. M. G. Jenda, On Gorenstein injective modules, Comm. Algebra 21 (1993), no. 10, 3489-3501. https://doi.org/10.1080/00927879308824744
  5. E. E. Enochs and O. M. G. Jenda, Gorenstein injective and projective modules, Math. Z. 220 (1995), no. 4, 611-633. https://doi.org/10.1007/BF02572634
  6. E. E. Enochs and O. M. G. Jenda, Relative homological algebra, De Gruyter Expositions in Mathematics, 30, Walter de Gruyter & Co., Berlin, 2000. https://doi.org/10.1515/9783110803662
  7. H.-B. Foxby, Gorenstein modules and related modules, Math. Scand. 31 (1972), 267-284 (1973). https://doi.org/10.7146/math.scand.a-11434
  8. H. Holm and P. Jorgensen, Semi-dualizing modules and related Gorenstein homological dimensions, J. Pure Appl. Algebra 205 (2006), no. 2, 423-445. https://doi.org/10.1016/j.jpaa.2005.07.010
  9. I. Kaplansky, Commutative Rings, revised edition, The University of Chicago Press, Chicago, IL, 1974.
  10. M. S. Osborne, Basic Homological Algebra, Graduate Texts in Mathematics, 196, Springer-Verlag, New York, 2000. https://doi.org/10.1007/978-1-4612-1278-2
  11. S. Park and E. Cho, Injective and projective properties of R[x]-modules, Czechoslovak Math. J. 54(129) (2004), no. 3, 573-578. https://doi.org/10.1007/s10587-004-6409-5
  12. J. J. Rotman, An introduction to homological algebra, Pure and Applied Mathematics, 85, Academic Press, Inc., New York, 1979.
  13. R. Sazeedeh, Strongly torsion free, copure flat and Matlis reflexive modules, J. Pure Appl. Algebra 192 (2004), no. 1-3, 265-274. https://doi.org/10.1016/j.jpaa.2004.01.010
  14. Z. P. Wang, S. T. Guo, and H. Y. Ma, Stability of Gorenstein modules with respect to semidualizing module, J. Math. 37 (2017), 1143-1153.
  15. F. Wang and H. Kim, Foundations of commutative rings and their modules, Algebra and Applications, 22, Springer, Singapore, 2016. https://doi.org/10.1007/978-981-10-3337-7
  16. X. Yang and Z. Liu, Strongly Gorenstein projective, injective and flat modules, J. Algebra 320 (2008), no. 7, 2659-2674. https://doi.org/10.1016/j.jalgebra.2008.07.006
  17. W. Zhang, Z. Liu, and X. Yang, Foxby equivalences associated to strongly Gorenstein modules, Kodai Math. J. 41 (2018), no. 2, 397-412. https://doi.org/10.2996/kmj/1530496849