DING-GRADED MODULES AND GORENSTEIN GR-FLAT MODULES
Glasgow mathematical journal, Tome 60 (2018) no. 2, pp. 339-360

Voir la notice de l'article provenant de la source Cambridge University Press

Let R be a graded ring. We introduce the concepts of Ding gr-injective and Ding gr-projective R-modules, which are the graded analogues of Ding injective and Ding projective modules. Several characterizations and properties of Ding gr-injective and Ding gr-projective modules are obtained. In addition, we investigate the relationships among Gorenstein gr-flat, Ding gr-injective and Ding gr-projective modules.
MAO, LIXIN. DING-GRADED MODULES AND GORENSTEIN GR-FLAT MODULES. Glasgow mathematical journal, Tome 60 (2018) no. 2, pp. 339-360. doi: 10.1017/S0017089517000155
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[1] 1. Asensio, M. J., Lopez Ramos, J. A. and Torrecillas, B., Gorenstein gr-injective and gr-projective modules, Comm. Algebra 26 (1998), 225–240. Google Scholar | DOI

[2] 2. Asensio, M. J., Lopez Ramos, J. A. and Torrecillas, B., Gorenstein gr-flat modules, Comm. Algebra 26 (1998), 3195–3209. Google Scholar

[3] 3. Asensio, M. J., Lopez Ramos, J. A. and Torrecillas, B., FP-gr-injective modules and gr-FC rings, Algebra Number Theory (Marcel Dekker, Inc., New York, 1999), 1–11. Google Scholar

[4] 4. Asensio, M. J., Lopez Ramos, J. A. and Torrecillas, B., Covers and envelopes over gr-Gorenstein rings, J. Algebra 215 (1999), 437–459. Google Scholar | DOI

[5] 5. Auslander, M. and Bridger, M., Stable module theory, Mem. Amer. Math. Soc., vol. 94 (American Mathematical Society, Providence, 1969). Google Scholar

[6] 6. Crivei, S., Prest, M., and Torrecillas, B., Covers in finitely accessible categories, Proc. Amer. Math. Soc. 138 (2010), 1213–1221. Google Scholar

[7] 7. Ding, N. Q., Li, Y. L. and Mao, L. X., Strongly Gorenstein flat modules, J. Aust. Math. Soc. 86 (2009), 323–338. Google Scholar | DOI

[8] 8. Enochs, E. E., Injective and flat covers, envelopes and resolvents, Israel J. Math. 39 (1981), 189–209. Google Scholar

[9] 9. Enochs, E. E. and Jenda, O. M. G., Gorenstein injective and Gorenstein projective modules, Math. Z. 220 (1995), 611–633. Google Scholar

[10] 10. Enochs, E. E. and Jenda, O. M. G., Relative homological algebra (Walter de Gruyter, Berlin-New York, 2000). Google Scholar

[11] 11. Enochs, E. E., Jenda, O. M. G. and Torrecillas, B., Gorenstein flat modules, Nanjing Daxue Xuebao Shuxue Bannian Kan 10 (1993), 1–9. Google Scholar

[12] 12. Enochs, E. E. and López-Ramos, J. A., Gorenstein flat modules (Nova Science Publishers, Inc., New York, 2001). Google Scholar

[13] 13. Enochs, E. E. and Oyonarte, L., Covers, envelopes and cotorsion theories (Nova Science Publishers, Inc., New York, 2002). Google Scholar

[14] 14. García Rozas, J. R., López-Ramos, J. A. and Torrecillas, B., On the existence of flat covers in R-gr, Comm. Algebra 29 (2001), 3341–3349. Google Scholar

[15] 15. Garcia Rozas, J. R. and Torrecillas, B., Preserving and reflecting covers by functors: Applications to graded modules, J. Pure Appl. Algebra 112 (1996), 91–107. Google Scholar

[16] 16. Gillespie, J., Cotorsion pairs and degreewise homological model structures, Homology, Homotopy Appl. 10 (2008), 283–304. Google Scholar | DOI

[17] 17. Gillespie, J., Model structures on modules over Ding-Chen rings, Homology, Homotopy Appl. 12 (2010), 61–73. Google Scholar

[18] 18. Göbel, R. and Trlifaj, J., Approximations and endomorphism algebras of modules (Walter de Gruyter, Berlin-New York, 2006). Google Scholar

[19] 19. Hermann, M., Ikeda, S. and Orbanz, U., Equimultiplicity and blowing up (Springer-Verlag, New York-Berlin, 1988). Google Scholar

[20] 20. Holm, H., Gorenstein homological dimensions, J. Pure Appl. Algebra 189 (2004), 167–193. Google Scholar

[21] 21. Malliavin, M. P., Sur les anneaux de groupes FP self-injectifs. C. R. Acad. Sc. Paris 273 (1971), 88–91. Google Scholar

[22] 22. Mao, L. X. and Ding, N. Q., Gorenstein FP-injective and Gorenstein flat modules, J. Algebra Appl. 7 (2008), 491–506. Google Scholar

[23] 23. Nastasescu, C., Raianu, S. and Van Oystaeyen, F., Modules graded by G-sets, Math. Z. 203 (1990), 605–627. Google Scholar

[24] 24. Nastasescu, C., Van Den Bergh, M. and Van Oystaeyen, F., Separable functors applied to graded rings, J. Algebra 123 (1989), 397–413. Google Scholar

[25] 25. Nastasescu, C. and Van Oystaeyen, F., Graded ring theory (North-Holland Publishing Company, Amsterdam, New York, Oxford, 1982). Google Scholar

[26] 26. Rotman, J. J., An introduction to homological algebra (Academic Press, New York, 1979). Google Scholar

[27] 27. Stenström, B., Coherent rings and FP-injective modules, J. London Math. Soc. 2 (1970), 323–329. Google Scholar

[28] 28. Stenström, B., Rings of quotients (Springer-Verlag, Berlin, Heidelberg, New York, 1975). Google Scholar

[29] 29. Wisbauer, R., Foundations of module and ring theory (Gordon and Breach, Philadelphia, 1991). Google Scholar

[30] 30. Yang, X. Y. and Liu, Z. K., FP-gr-injective modules, Math. J. Okayama Univ. 53 (2011), 83–100. Google Scholar

[31] 31. Yang, G., Liu, Z. K. and Liang, L., Ding projective and ding injective modules, Algebra Colloq. 20 (2013), 601–612. Google Scholar

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