RESOLUTIONS AND DIMENSIONS OF RELATIVE INJECTIVE MODULES AND RELATIVE FLAT MODULES

Title & Authors
RESOLUTIONS AND DIMENSIONS OF RELATIVE INJECTIVE MODULES AND RELATIVE FLAT MODULES
Zeng, Yuedi; Chen, Jianlong;

Abstract
Let m and n be fixed positive integers and M a right R-module. Recall that M is said to be ($\small{m}$, $\small{n}$)-injective if $\small{Ext^1}$(P, M)
Keywords
(m, n)-coherent ring;(m, n)-injective module;(m, n)-flat module;(pre)cover;(pre)envelope;
Language
English
Cited by
References
1.
F. W. Anderson and K. R. Fuller, Rings and Categries of Modules, Second edition, Springer-Verlag, Berlin, 1974.

2.
T. J. Cheatham and D. R. Stone, Flat and projective character modules, Proc. Amer. Math. Soc. 81 (1981), no. 2, 175-177.

3.
J. L. Chen and N. Q. Ding, The weak global dimension of commutative coherent rings, Comm. Algebra 21 (1993), no. 10, 3521-3528.

4.
J. L. Chen, N. Q. Ding, Y. L. Li, and Y. Q. Zhou, On (m, n)-injectivity of modules, Comm. Algebra 29 (2001), no. 12, 5589-5603.

5.
R. R. Colby, Rings which have flat injective modules, J. Algebra 35 (1975), 239-252.

6.
N. Q. Ding, On envelopes with the unique mapping property, Comm. Algebra 24 (1996), no. 4, 1459-1470.

7.
E. E. Enochs, Injective and flat covers, envelopes and resolvents, Israel J. Math. 39 (1981), no. 3, 189-209.

8.
E. E. Enochs and O. M. G. Jenda, Relative Homological Algebra, de Gruyter Exp. Math., vol 30, de Gruyter Berlin, 2000.

9.
L. Fuchs and L. Salce, Modules over Non-Noetherian Domains, Math. Surveys and Monographs. Vol. 84. Providence, Amer. Math. Society, 2001.

10.
R. Gobel and J. Trlifaj, Approximations and Endomorphism Algebras of Modules, GEM 41. Berlin-New York, Walter de Gruyter, 2006.

11.
H. Holm and P. Jorgensen, Covers, precovers and purity, Illinois J. Math. 52 (2008), no. 2, 691-703.

12.
L. X. Mao and N. Q. Ding, On relative injective modules and relative coherent rings, Comm. Algebra 34 (2006), no. 7, 2531-2545.

13.
L. X. Mao and N. Q. Ding, On divisible and torsionfree modules, Comm. Algebra 36 (2008), no. 2, 708-731.

14.
W. K. Nicholson and E. Sanchez Campos, Rings with the dual of the isomorphism theorem, J. Algebra 271 (2004), no. 1, 391-406.

15.
A. Shamsuddin, n-injective and n-flat modules, Comm. Algebra 29 (2001), no. 5, 2039-2050.

16.
J. Xu, Flat Covers of Modules, Lecture Notes in Math. 1634. Berlin-Heidelberg-New York, Springer-Verlag, 1996.

17.
X. X. Zhang and J. L. Chen, On (m, n)-injective modules and (m, n)-coherent rings, Algebra Colloq. 12 (2005), no. 1, 149-160.

18.
H. Y. Zhu and N. Q. Ding, Generalized morphic rings and their applications, Comm. Algebra 35 (2007), no. 9, 2820-2837.

19.
Z. Zhu, J. L. Chen, and X. X. Zhang, On (m, n)-purity of modules, East-West J. Math. 5 (2003), no. 1, 35-44.