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http://dx.doi.org/10.4134/JKMS.2012.49.1.031

HOMOLOGICAL PROPERTIES OF MODULES OVER DING-CHEN RINGS  

Yang, Gang (School of Mathematics Physics and Software Engineering Lanzhou Jiaotong University)
Publication Information
Journal of the Korean Mathematical Society / v.49, no.1, 2012 , pp. 31-47 More about this Journal
Abstract
The so-called Ding-Chen ring is an n-FC ring which is both left and right coherent, and has both left and right self FP-injective dimensions at most n for some non-negative integer n. In this paper, we investigate the classes of the so-called Ding projective, Ding injective and Gorenstein at modules and show that some homological properties of modules over Gorenstein rings can be generalized to the modules over Ding-Chen rings. We first consider Gorenstein at and Ding injective dimensions of modules together with Ding injective precovers. We then discuss balance of functors Hom and tensor.
Keywords
Ding-Chen ring; Ding projective and Ding injective module; Gorenstein flat module; precover; preenvelope; balanced functors;
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1 M. Hovey, Cotorsion pairs, model category structures, and representation theory, Math. Z. 241 (2002), no. 3, 553-592.   DOI
2 Y. Iwanaga, On rings with nite self-injective dimension, Comm. Algebra 7 (1979), no. 4, 393-414.   DOI   ScienceOn
3 Y. Iwanaga, On rings with finite self-injective dimension II, Tsukuba J. Math. 4 (1980), no. 1, 107-113.   DOI
4 L. X. Mao and N. Q. Ding, Gorenstein FP-injective and Gorenstein at modules, J. Algebra Appl. 7 (2008), no. 4, 491-506.   DOI   ScienceOn
5 L. X. Mao and N. Q. Ding, Envelopes and covers by modules of finite FP-injective and flat dimensions, Comm. Algebra 35 (2007), no. 3, 833-849.   DOI   ScienceOn
6 W. L. Song and Z. Y. Huang, Gorenstein atness and injectivity over Gorenstein rings, Sci. China Ser. A 51 (2008), no. 2, 215-218.   DOI   ScienceOn
7 B. Stenstrom, Coherent rings and FP-injective modules, J. London Math. Soc. 2 (1970), no. 2, 323-329.   DOI
8 J. Z. Xu, Flat Covers of Modules, Lecture Notes in Math, 1634, 1996.
9 G. Yang and Z. K. Liu, Gorenstein flat covers over GF-closed rings, Comm. Algebra, to appear.
10 N. Q. Ding, Y. L. Li, and L. X. Mao, Strongly Gorenstein at modules, J. Aust. Math. Soc. 86 (2009), no. 3, 323-338.   DOI
11 N. Q. Ding and L. X. Mao, Relative FP-projective modules, Comm. Algebra 33 (2005), no. 5, 1587-1602.   DOI   ScienceOn
12 E. E. Enochs and O. M. G. Jenda, Balanced functors applied to modules, J. Algebra 92 (1985), 303-310.   DOI
13 E. E. Enochs, Injective and at covers, envelopes and resolvents, Israel J. Math. 39 (1981), no. 3, 189-209.   DOI
14 E. E. Enochs, S. Estrada, and B. Torrecillas, Gorenstein flat covers and gorenstein cotorsion modules over integral group rings, Algebr. Represent. Theory 8 (2005), no. 4, 525{539.   DOI
15 E. E. Enochs and Z. Y. Huang, Injective envelopes and (Gorenstein) at covers, in press.
16 E. E. Enochs and O. M. G. Jenda, Gorenstein balance of Hom and tensor, Tsukuba J. Math. 19 (1995), no. 1, 1-13.   DOI
17 E. E. Enochs and O. M. G. Jenda, Relative Homological Algebra, De Gruyter Expositions in Mathematics no. 30, Walter De Gruyter, New York, 2000.
18 E. E. Enochs, O. M. G. Jenda, and J. A. Lopez-Ramos, The existence of Gorenstein flat covers, Math. Scand. 94 (2004), no. 1, 46-62.   DOI
19 E. E. Enochs, O. M. G. Jenda, and B. Torrecillas, Gorenstein flat modules, Nanjing Daxue Xuebao Shuxue Bannian Kan, 10 (1993), no. 1, 1-9.
20 J. Gillespie, Model structures on modules over Ding-Chen rings, Homology, Homotopy Appl. 12 (2010), no. 1, 61-73.   DOI
21 H. Holm, Gorenstein homological dimensions, J. Pure Appl. Algebra 189 (2004), no. 1-3, 167-193.   DOI   ScienceOn
22 H. Holm, Gorenstein derived functors, Proc. Amer. Math. Soc. 132 (2004), no. 7, 1913-1923.   DOI   ScienceOn
23 N. Q. Ding and J. L. Chen, The flat dimensions of injective modules, Manuscripta Math. 78 (1993), no. 2, 165-177.   DOI
24 M. Auslander and M. Bridger, Stable Module Theory, Memoirs of the American Mathematical Society, No. 94 American Mathematical Society, Providence, R.I. 1969.
25 D. Bennis, Rings over which the class of Gorenstein at modules is closed under extensions, Comm. Algebra, 37 (2009), no. 3, 855-868.   DOI   ScienceOn
26 R. F. Damiano, Coflat rings and modules, Pacific J. Math. 81 (1979), no. 2, 349-369.   DOI
27 N. Q. Ding and J. L. Chen, The homological dimensions of simple modules, Bull. Aust. Math. Soc. 48 (1993), no. 2, 265-274.   DOI
28 N. Q. Ding and J. L. Chen, Coherent rings with finite self-FP-injective dimension, Comm. Algebra 24 (1996), no. 9, 2963-2980.   DOI   ScienceOn