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ON DUAL BAER MODULES

Published online by Cambridge University Press:  25 November 2009

DERYA KESKIN TÜTÜNCÜ  and
RACHID TRIBAK
DERYA KESKIN TÜTÜNCÜ
Affiliation:
Department of Mathematics, Hacettepe University, 06800 Beytepe, Ankara, Turkey e-mail: keskin@hacettepe.edu.tr
RACHID TRIBAK
Affiliation:
Département de Mathématiques, Faculté des Sciences de Tétouan, B.P 21.21. Tétouan, Morocco e-mail: tribak12@yahoo.com
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Abstract

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In this paper we introduce -non-cosingular modules, dual Baer modules and -modules. We prove that a module M is lifting and -non-cosingular if and only if it is a dual Baer and -module. Rings for which all modules are dual Baer are precisely determined. We also give a necessary condition for a finite direct sum of dual Baer modules to be dual Baer.

Keywords

16D1016D8016E60
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 52 , Issue 2 , May 2010 , pp. 261 - 269
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

REFERENCES

1.Camps, R. and Dicks, W., On semi-local rings, Israel J. Math. 81 (1993), 203–211.CrossRefGoogle Scholar
2.Clark, J., Lomp, C., Vanaja, N. and Wisbauer, R., Lifting modules, in Supplements and Projectivity in Module Theory Series: Frontiers in Mathematics (Birkhauser Verlag, Basel-Boston-Berlin, 2006).Google Scholar
3.Facchini, A., Module theory: Endomorphism rings and direct sum decompositions in some classes of modules (Birkhauser, Basel-Boston-Berlin, 1998).Google Scholar
4.Ganesan, L. and Vanaja, N., Modules for which every submodule has a unique coclosure, Commun. Algebra 30 (5) (2002), 2355–2377.CrossRefGoogle Scholar
5.Garcia, J. L., Properties of direct summands of modules, Commun. Algebra 17 (1) (1989), 73–92.CrossRefGoogle Scholar
6.Idelhadj, A. and Tribak, R., Modules for which every submodule has a supplement that is a direct summand, Arab. J. Sci. Eng. Sect. C Theme Issues 25 (2) (2000), 179–189.Google Scholar
7.Kaplansky, I., Modules over Dedekind rings and valuation rings, Trans. Amer. Math. Soc. 72 (1952), 327–340.CrossRefGoogle Scholar
8.Kasch, F., Modules and rings (Academic Press, New York, 1982).Google Scholar
9.Lam, T. Y., Lectures on modules and rings (Springer-Verlag, New York, 1999).CrossRefGoogle Scholar
10.Mohamed, S. H. and Müller, B. J., Continuous and discrete modules (London Math. Soc. LNS 147: Cambridge University Press, England, UK, 1990).CrossRefGoogle Scholar
11.Rizvi, S. T. and Roman, C. S., Baer and quasi-Baer modules, Commun. Algebra 32 (1) (2004), 103–123.CrossRefGoogle Scholar
12.Rizvi, S. T. and Roman, C. S., On -nonsingular modules and applications, Commun. Algebra 35 (2007), 1–22.CrossRefGoogle Scholar
13.Sharpe, D. W. and Vamos, P., Injective modules (Cambridge University Press, England, UK, 1972).Google Scholar
14.Talebi, Y. and Vanaja, N., Torsion theory cogenerated by M-small modules, Commun. Algebra 30 (3) (2002), 1449–1460.CrossRefGoogle Scholar
15.Wisbauer, R., Foundations of module and ring theory (Gordon and Breach, Reading, PA, 1991).Google Scholar