과제정보
This work was supported by National Natural Science Foundation of China (No. 11761061).
참고문헌
- M. Auslander and M. Bridger, Stable module theory, Memoirs of the American Mathematical Society, No. 94, American Mathematical Society, Providence, RI, 1969.
- H. Bass, Injective dimension in Noetherian rings, Trans. Amer. Math. Soc. 102 (1962), 18-29. https://doi.org/10.2307/1993878
- 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
- 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
- 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
- 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
- H.-B. Foxby, Gorenstein modules and related modules, Math. Scand. 31 (1972), 267-284 (1973). https://doi.org/10.7146/math.scand.a-11434
- 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
- I. Kaplansky, Commutative Rings, revised edition, The University of Chicago Press, Chicago, IL, 1974.
- 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
- 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
- J. J. Rotman, An introduction to homological algebra, Pure and Applied Mathematics, 85, Academic Press, Inc., New York, 1979.
- 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
- 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.
- 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
- 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
- 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