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Title: $C$-Gorenstein projective, injective and flat modules (English)
Author: Yang, Xiao Yan
Author: Liu, Zhong Kui
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 60
Issue: 4
Year: 2010
Pages: 1109-1129
Summary lang: English
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Category: math
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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. (English)
Keyword: $C$-Gorenstein projective module
Keyword: $C$-Gorenstein injective module
Keyword: $C$-Gorenstein flat module
MSC: 13D07
MSC: 16E65
idZBL: Zbl 1224.13014
idMR: MR2738973
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Date available: 2010-11-20T14:01:51Z
Last updated: 2020-07-03
Stable URL: http://hdl.handle.net/10338.dmlcz/140810
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Reference: [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. Zbl 1104.13008, MR 2236602, 10.1016/j.jalgebra.2005.12.007
Reference: [2] Enochs, E. E., Jenda, O. M. G.: Relative Homological Algebra, de Gruyter Exp. Math. Walter de Gruyter and Co., Berlin.(2000). MR 1753146
Reference: [3] Enochs, E. E., Iacos, A., Jenda, O. M. G.: Closure under transfinite extensions.Illinois J. Math. 51 (2007), 561-569. MR 2342674, 10.1215/ijm/1258138429
Reference: [4] Holm, H.: Gorenstein homological dimensions.J. Pure Appl. Algebra 189 (2004), 167-193. Zbl 1050.16003, MR 2038564, 10.1016/j.jpaa.2003.11.007
Reference: [5] Holm, H., Jørgensen, P.: Cohen-Macaulay homological dimensions.Rend. Semin. Mat. Univ. Padova 117 (2007), 87-112. MR 2351787
Reference: [6] Holm, H., Jørgensen, P.: Semi-dualizing modules and related Gorenstein homological dimensions.J. Pure Appl. Algebra 205 (2006), 423-445. MR 2203625, 10.1016/j.jpaa.2005.07.010
Reference: [7] Holm, H., White, D.: Foxby equivalence over associative rings.J. Math. Kyoto Univ. 47 (2007), 781-808. Zbl 1154.16007, MR 2413065, 10.1215/kjm/1250692289
Reference: [8] Kasch, F.: Modules and Rings.London Math. Soc. Monogr. Academic press, London (1981). Zbl 0527.16001, MR 0667346
Reference: [9] Lam, T. Y.: Lecture on Modules and Rings.Springer Verlag, New York (1999). MR 1653294
Reference: [10] Yang, X., Liu, Z.: Gorenstein projective, injective and flat modules.J. Aust. Math. Soc 87 (2009), 395-407. MR 2576573, 10.1017/S1446788709000093
Reference: [11] Osborne, M. S.: Basic Homological Algebra.Graduate Texts in Mathematics, Springer, New York, Berlin (2000). Zbl 0948.18001, MR 1757274
Reference: [12] Park, S., Pusan, E. C.: Injective and projective properties of $R[x]$-modules.Czech. Math. J. 54 (2004), 573-578. MR 2086717, 10.1007/s10587-004-6409-5
Reference: [13] Rotman, J. J.: An Introductions to Homological Algebra.Academic Press, New York (1979). MR 0538169
Reference: [14] Sazeedeh, R.: Strongly torsion free, copure flat and Matlis reflexive modules.J. Pure Appl. Algebra 192 (2004), 265-274. Zbl 1087.13004, MR 2067199, 10.1016/j.jpaa.2004.01.010
Reference: [15] Trlifaj, J.: Ext and inverse limits.Illinois J. Math. 47 (2003), 529-538. Zbl 1035.16006, MR 2031338, 10.1215/ijm/1258488170
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