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THE CLASS OF MODULES WITH PROJECTIVE COVER
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 Title & Authors
THE CLASS OF MODULES WITH PROJECTIVE COVER
Guo, Yong-Hua;
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 Abstract
Let R be a ring. A right R-module M is called perfect if M possesses a projective cover. In this paper, we consider the relationship between the class of perfect modules and other classes of modules. Some known rings are characterized by these relationships.
 Keywords
projective cover;-hereditary ring;perfect ring;small submodule;
 Language
English
 Cited by
1.
Rings Whose Nonsingular Modules Have Projective Covers, Ukrainian Mathematical Journal, 2016, 68, 1, 1  crossref(new windwow)
2.
ON A SPECIAL CLASS OF EXACT SEQUENCES, Journal of Algebra and Its Applications, 2011, 10, 05, 915  crossref(new windwow)
3.
EXISTENCE OF ALMOST SPLIT SEQUENCES VIA REGULAR SEQUENCES, Bulletin of the Australian Mathematical Society, 2013, 88, 02, 218  crossref(new windwow)
 References
1.
F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Second edition. Graduate Texts in Mathematics, 13. Springer-Verlag, New York, 1992.

2.
G. Azumaya and A. Facchini, Rings of pure global dimension zero and Mittag-Leffler modules, J. Pure Appl. Algebra 62 (1989), no. 2, 109-122. crossref(new window)

3.
H. Bass, Finitistic dimension and a homological generalization of semi-primary rings, Trans. Amer. Math. Soc. 95 (1960), 466-488. crossref(new window)

4.
H. Cartan and S. Eilenberg, Homological Algebra, Princeton Univ. Press, Princeton, 1956.

5.
J. Clark, C. Lomp, N. Vanaja, and R. Wisbauer, Lifting Modules, Supplements and projectivity in module theory. Frontiers in Mathematics. Birkhauser Verlag, Basel, 2006.

6.
D. J. Fieldhouse, Characterizations of modules, Canad. J. Math. 23 (1971), 608-610. crossref(new window)

7.
T. H. Fay and S. V. Joubert, Relative injectivity, Chinese J. Math. 22 (1994), no. 1, 65-94.

8.
K. R. Goodeal, Ring Theory: Nonsingular Rings and Modules, Pure and Applied Math-ematics, No. 33. Marcel Dekker, Inc., New York-Basel, 1976.

9.
P. A. Guil Asensio and I. Herzog, Sigma-cotorsion rings, Adv. Math. 191 (2005), no. 1, 11-28. crossref(new window)

10.
S.-T. Hu, Introduction to Homological Algebra, Holden-Day, Inc., San Francisco, Calif.- London-Amsterdam 1968.

11.
T. Y. Lam, A First Course in Noncommutative Rings, Graduate Texts in Mathematics, 131. Springer-Verlag, New York, 1991.

12.
T. Y. Lam, Lectures on Modules and Rings, Graduate Texts in Mathematics, 189. Springer- Verlag, New York, 1999.

13.
L. X. Mao and N. Q. Ding, Notes on cotorsion modules, Comm. Algebra 33 (2005), no.1, 349-360. crossref(new window)

14.
J. J. Rotman, An Introduction to Homological Algebra, Pure and Applied Mathematics, 85. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1979.

15.
F. L. Sandomierski, Homological dimensions under change of rings, Math. Z. 130(1973), 55-65. crossref(new window)

16.
F. L. Sandomierski, On semiperfect and perfect ring, Proc. Amer. Math. Soc. 21 (1969), no. 1, 205-207.

17.
L. Shen and J. L. Chen, New characterizations of quasi-Frobenius rings, Comm. Algebra 34 (2006), no. 6, 2157-2165. crossref(new window)

18.
U. Shukla, On the projective cover of a module and related results, Pacific J. Math. 12 (1962), 709-717. crossref(new window)

19.
J. Xu, Flat Covers of Modules, Lecture Notes in Mathematics, 1634. Springer-Verlag, Berlin, 1996.

20.
D. Zhou, Rings characterized by a class of modules, Comm. Algebra 33 (2005), no. 9, 2941-2955. crossref(new window)