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Keywords:
$C$-Gorenstein projective module; $C$-Gorenstein injective module; $C$-Gorenstein flat module
Summary:
By analogy with the projective, injective and flat modules, in this paper we study some properties of $C$-Gorenstein projective, injective and flat modules and discuss some connections between $C$-Gorenstein injective and $C$-Gorenstein flat modules. We also investigate some connections between $C$-Gorenstein projective, injective and flat modules of change of rings.
References:
[1] Christensen, L. W., Frankild, A., Holm, H.: On Gorenstein projective, injective and flat dimensions---a functorial description with applications. J. Algebra 302 (2006), 231-279. DOI 10.1016/j.jalgebra.2005.12.007 | MR 2236602 | Zbl 1104.13008
[2] Enochs, E. E., Jenda, O. M. G.: Relative Homological Algebra, de Gruyter Exp. Math. Walter de Gruyter and Co., Berlin. (2000). MR 1753146
[3] Enochs, E. E., Iacos, A., Jenda, O. M. G.: Closure under transfinite extensions. Illinois J. Math. 51 (2007), 561-569. DOI 10.1215/ijm/1258138429 | MR 2342674
[4] Holm, H.: Gorenstein homological dimensions. J. Pure Appl. Algebra 189 (2004), 167-193. DOI 10.1016/j.jpaa.2003.11.007 | MR 2038564 | Zbl 1050.16003
[5] Holm, H., Jørgensen, P.: Cohen-Macaulay homological dimensions. Rend. Semin. Mat. Univ. Padova 117 (2007), 87-112. MR 2351787
[6] Holm, H., Jørgensen, P.: Semi-dualizing modules and related Gorenstein homological dimensions. J. Pure Appl. Algebra 205 (2006), 423-445. DOI 10.1016/j.jpaa.2005.07.010 | MR 2203625
[7] Holm, H., White, D.: Foxby equivalence over associative rings. J. Math. Kyoto Univ. 47 (2007), 781-808. DOI 10.1215/kjm/1250692289 | MR 2413065 | Zbl 1154.16007
[8] Kasch, F.: Modules and Rings. London Math. Soc. Monogr. Academic press, London (1981). MR 0667346 | Zbl 0527.16001
[9] Lam, T. Y.: Lecture on Modules and Rings. Springer Verlag, New York (1999). MR 1653294
[10] Yang, X., Liu, Z.: Gorenstein projective, injective and flat modules. J. Aust. Math. Soc 87 (2009), 395-407. DOI 10.1017/S1446788709000093 | MR 2576573
[11] Osborne, M. S.: Basic Homological Algebra. Graduate Texts in Mathematics, Springer, New York, Berlin (2000). MR 1757274 | Zbl 0948.18001
[12] Park, S., Pusan, E. C.: Injective and projective properties of $R[x]$-modules. Czech. Math. J. 54 (2004), 573-578. DOI 10.1007/s10587-004-6409-5 | MR 2086717
[13] Rotman, J. J.: An Introductions to Homological Algebra. Academic Press, New York (1979). MR 0538169
[14] Sazeedeh, R.: Strongly torsion free, copure flat and Matlis reflexive modules. J. Pure Appl. Algebra 192 (2004), 265-274. DOI 10.1016/j.jpaa.2004.01.010 | MR 2067199 | Zbl 1087.13004
[15] Trlifaj, J.: Ext and inverse limits. Illinois J. Math. 47 (2003), 529-538. DOI 10.1215/ijm/1258488170 | MR 2031338 | Zbl 1035.16006
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