DOI QR코드

DOI QR Code

THE CLASS OF MODULES WITH PROJECTIVE COVER

  • Guo, Yong-Hua (DEPARTMENT OF MATHEMATICS NANJING UNIVERSITY, DEPARTMENT OF MATHEMATICS GUANGXI NORMAL UNIVERSITY)
  • Published : 2009.01.31

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

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. https://doi.org/10.1016/0022-4049(89)90146-1
  3. H. Bass, Finitistic dimension and a homological generalization of semi-primary rings, Trans. Amer. Math. Soc. 95 (1960), 466-488. https://doi.org/10.2307/1993568
  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. https://doi.org/10.4153/CJM-1971-068-1
  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. https://doi.org/10.1016/j.aim.2004.01.006
  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. https://doi.org/10.1081/AGB-200041029
  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. https://doi.org/10.1007/BF01178976
  16. F. L. Sandomierski, On semiperfect and perfect ring, Proc. Amer. Math. Soc. 21 (1969), no. 1, 205-207. https://doi.org/10.1090/S0002-9939-1969-0237567-5
  17. L. Shen and J. L. Chen, New characterizations of quasi-Frobenius rings, Comm. Algebra 34 (2006), no. 6, 2157-2165. https://doi.org/10.1080/00927870600549667
  18. U. Shukla, On the projective cover of a module and related results, Pacific J. Math. 12 (1962), 709-717. https://doi.org/10.2140/pjm.1962.12.709
  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. https://doi.org/10.1081/AGB-200066197

Cited by

  1. ON A SPECIAL CLASS OF EXACT SEQUENCES vol.10, pp.05, 2011, https://doi.org/10.1142/S021949881100504X
  2. Rings Whose Nonsingular Modules Have Projective Covers vol.68, pp.1, 2016, https://doi.org/10.1007/s11253-016-1204-7
  3. EXISTENCE OF ALMOST SPLIT SEQUENCES VIA REGULAR SEQUENCES vol.88, pp.02, 2013, https://doi.org/10.1017/S0004972713000099