Geodesic
ON DUAL BAER MODULES
Glasgow mathematical journal, Tome 52 (2010) no. 2, pp. 261-269

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.1017/S0017089509990334
Mots-clés : 16D10, 16D80, 16E60 
TÜTÜNCÜ, DERYA KESKIN; TRIBAK, RACHID. ON DUAL BAER MODULES. Glasgow mathematical journal, Tome 52 (2010) no. 2, pp. 261-269. doi: 10.1017/S0017089509990334
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     year = {2010},
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     doi = {10.1017/S0017089509990334},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089509990334/}
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[1] 1.Camps, R. and Dicks, W., On semi-local rings, Israel J. Math. 81 (1993), 203–211. Google Scholar | DOI

[2] 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] 3.Facchini, A., Module theory: Endomorphism rings and direct sum decompositions in some classes of modules (Birkhauser, Basel-Boston-Berlin, 1998). Google Scholar

[4] 4.Ganesan, L. and Vanaja, N., Modules for which every submodule has a unique coclosure, Commun. Algebra 30 (5) (2002), 2355–2377. Google Scholar | DOI

[5] 5.Garcia, J. L., Properties of direct summands of modules, Commun. Algebra 17 (1) (1989), 73–92. Google Scholar | DOI

[6] 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] 7.Kaplansky, I., Modules over Dedekind rings and valuation rings, Trans. Amer. Math. Soc. 72 (1952), 327–340. Google Scholar | DOI

[8] 8.Kasch, F., Modules and rings (Academic Press, New York, 1982). Google Scholar

[9] 9.Lam, T. Y., Lectures on modules and rings (Springer-Verlag, New York, 1999). Google Scholar | DOI

[10] 10.Mohamed, S. H. and Müller, B. J., Continuous and discrete modules (London Math. Soc. LNS 147: Cambridge University Press, England, UK, 1990). Google Scholar | DOI

[11] 11.Rizvi, S. T. and Roman, C. S., Baer and quasi-Baer modules, Commun. Algebra 32 (1) (2004), 103–123. Google Scholar | DOI

[12] 12.Rizvi, S. T. and Roman, C. S., On -nonsingular modules and applications, Commun. Algebra 35 (2007), 1–22. Google Scholar | DOI

[13] 13.Sharpe, D. W. and Vamos, P., Injective modules (Cambridge University Press, England, UK, 1972). Google Scholar

[14] 14.Talebi, Y. and Vanaja, N., Torsion theory cogenerated by M-small modules, Commun. Algebra 30 (3) (2002), 1449–1460. Google Scholar | DOI

[15] 15.Wisbauer, R., Foundations of module and ring theory (Gordon and Breach, Reading, PA, 1991). Google Scholar

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