JOURNAL BROWSE
Search
Advanced SearchSearch Tips
HOMOLOGICAL PROPERTIES OF MODULES OVER DING-CHEN RINGS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
HOMOLOGICAL PROPERTIES OF MODULES OVER DING-CHEN RINGS
Yang, Gang;
  PDF(new window)
 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;
 Language
English
 Cited by
1.
RELATIVE AND TATE COHOMOLOGY OF DING MODULES AND COMPLEXES,;

대한수학회지, 2015. vol.52. 4, pp.821-838 crossref(new window)
1.
Relative left derived functors of tensor product functors, Acta Mathematica Sinica, English Series, 2016, 32, 7, 753  crossref(new windwow)
2.
On Ding homological dimensions, Applied Mathematics-A Journal of Chinese Universities, 2015, 30, 4, 491  crossref(new windwow)
3.
RELATIVE AND TATE COHOMOLOGY OF DING MODULES AND COMPLEXES, Journal of the Korean Mathematical Society, 2015, 52, 4, 821  crossref(new windwow)
4.
DERIVED CATEGORIES WITH RESPECT TO DING MODULES, Journal of Algebra and Its Applications, 2013, 12, 06, 1350021  crossref(new windwow)
 References
1.
M. Auslander and M. Bridger, Stable Module Theory, Memoirs of the American Mathematical Society, No. 94 American Mathematical Society, Providence, R.I. 1969.

2.
D. Bennis, Rings over which the class of Gorenstein at modules is closed under extensions, Comm. Algebra, 37 (2009), no. 3, 855-868. crossref(new window)

3.
R. F. Damiano, Coflat rings and modules, Pacific J. Math. 81 (1979), no. 2, 349-369. crossref(new window)

4.
N. Q. Ding and J. L. Chen, The flat dimensions of injective modules, Manuscripta Math. 78 (1993), no. 2, 165-177. crossref(new window)

5.
N. Q. Ding and J. L. Chen, The homological dimensions of simple modules, Bull. Aust. Math. Soc. 48 (1993), no. 2, 265-274. crossref(new window)

6.
N. Q. Ding and J. L. Chen, Coherent rings with finite self-FP-injective dimension, Comm. Algebra 24 (1996), no. 9, 2963-2980. crossref(new window)

7.
N. Q. Ding, Y. L. Li, and L. X. Mao, Strongly Gorenstein at modules, J. Aust. Math. Soc. 86 (2009), no. 3, 323-338. crossref(new window)

8.
N. Q. Ding and L. X. Mao, Relative FP-projective modules, Comm. Algebra 33 (2005), no. 5, 1587-1602. crossref(new window)

9.
E. E. Enochs, Injective and at covers, envelopes and resolvents, Israel J. Math. 39 (1981), no. 3, 189-209. crossref(new window)

10.
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. crossref(new window)

11.
E. E. Enochs and Z. Y. Huang, Injective envelopes and (Gorenstein) at covers, in press.

12.
E. E. Enochs and O. M. G. Jenda, Balanced functors applied to modules, J. Algebra 92 (1985), 303-310. crossref(new window)

13.
E. E. Enochs and O. M. G. Jenda, Gorenstein balance of Hom and tensor, Tsukuba J. Math. 19 (1995), no. 1, 1-13.

14.
E. E. Enochs and O. M. G. Jenda, Relative Homological Algebra, De Gruyter Expositions in Mathematics no. 30, Walter De Gruyter, New York, 2000.

15.
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.

16.
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.

17.
J. Gillespie, Model structures on modules over Ding-Chen rings, Homology, Homotopy Appl. 12 (2010), no. 1, 61-73. crossref(new window)

18.
H. Holm, Gorenstein homological dimensions, J. Pure Appl. Algebra 189 (2004), no. 1-3, 167-193. crossref(new window)

19.
H. Holm, Gorenstein derived functors, Proc. Amer. Math. Soc. 132 (2004), no. 7, 1913-1923. crossref(new window)

20.
M. Hovey, Cotorsion pairs, model category structures, and representation theory, Math. Z. 241 (2002), no. 3, 553-592. crossref(new window)

21.
Y. Iwanaga, On rings with nite self-injective dimension, Comm. Algebra 7 (1979), no. 4, 393-414. crossref(new window)

22.
Y. Iwanaga, On rings with finite self-injective dimension II, Tsukuba J. Math. 4 (1980), no. 1, 107-113.

23.
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. crossref(new window)

24.
L. X. Mao and N. Q. Ding, Gorenstein FP-injective and Gorenstein at modules, J. Algebra Appl. 7 (2008), no. 4, 491-506. crossref(new window)

25.
W. L. Song and Z. Y. Huang, Gorenstein atness and injectivity over Gorenstein rings, Sci. China Ser. A 51 (2008), no. 2, 215-218. crossref(new window)

26.
B. Stenstrom, Coherent rings and FP-injective modules, J. London Math. Soc. 2 (1970), no. 2, 323-329. crossref(new window)

27.
J. Z. Xu, Flat Covers of Modules, Lecture Notes in Math, 1634, 1996.

28.
G. Yang and Z. K. Liu, Gorenstein flat covers over GF-closed rings, Comm. Algebra, to appear.