ON THE MIN-PROJECTIVE MODULES

Abstract

Let R be a commutative ring. An R-module M is called minprojective if Ext1R(M,RI) = 0, for every simple ideal I. In this paper, we first give some results of min-projective R-modules on the some specific rings such as cotorsion rings, von Neumann regular rings and coherent rings. Then we investigate min-projective covers on universally min-projective rings. Finally, we deal with some characterizations of min-projective modules over a perfect ring.

Keywords

• min-projective modules, min-flat modules, universally min-projective rings

References

1. F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Spriger- Verlag, New York, 1974.
2. N. Q. Ding and L. X. Mao, FP-projective dimensions, Comm. Algebra, 33 (2005), 1153–1170.
3. N. Q. Ding and L. X. Mao, Min-flat modules and min-coherent rings, Comm. Algebra, 36 (2007), 635–650.
4. N. Q. Ding and L. X. Mao, Notes on F P -projective modules and F P -injective modules, Advances in ring theory, 151–166, World Sci.Publ., Hackensack, NJ, N. Q. Ding and L. X. Mao, Notes on the cotorsion modules, Comm. Algebra, (2005), 349–360.
5. E. E. Enochs and M. G. Jenda, Relative Homological Algebra, Walter de Gruyter, Berlin, New York, 2000.
6. P. A. Guil Asensio and I. Herzog, Left cotorsion rings, Bull. London Math. Soc., 36 (2004) 303-309.
7. T. Y. Lam, A First Course in Non-Commutative Rings, Springer-Verlag, New York, 1991.
8. T. Y. Lam, Lectures on Modules and Rings, Springer-Verlag, Berlin, 1999.

9. M. J. Nikmehr, F. Shaveisi and R. Nikandish, n-Projective modules, Algebras, Groups and Geometries, 24 (2007), 447–454.
10. M. J. Nikmehr and F. Shaveisi, T -dimension and (n+1, T )-Projective modules, Southeast Asian Bull. Math., 35 (2011), 1–11.
11. J.J. Rotman, An Introduction to Homological Algebra, Academic Press, New York, 1979.
12. F. L. Sandomierski, Homological dimensions under change of rings, Math.Z., (1973), 55–65.
13. R. Wisbauer, Foundation of Module and Ring Theory, Gordon and Breach Publishers, 1991.
14. J. Xu, Flat covers of modules, Lecture Notes in Mathematics, 1643, Berlin, Springer-Verlag, 1996. M. Amini
15. Department of Mathematics Faculty of Science Payame Noor University Sonqor, Iran e-mail: [e-mail] A. Farajzadeh
16. Islamic Azad university Kermanshah Branch, Iran e-mail: [e-mail] S. Bayati
17. Department of Mathematics Faculty of Science Payame Noor University Sonqor, Iran e-mail: [e-mail]