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ON DIFFERENT NOTIONS OF TRANSITIVITY FOR QTAG-MODULES
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  • Journal title : Honam Mathematical Journal
  • Volume 38, Issue 2,  2016, pp.259-267
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2016.38.2.259
 Title & Authors
ON DIFFERENT NOTIONS OF TRANSITIVITY FOR QTAG-MODULES
Sikander, Fahad; Hasan, Ayazul; Mehdi, Alveera;
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 Abstract
A module M over an associative ring R with unity is a QTAG-module if every finitely generated submodule of any homomorphic image of M is a direct sum of uniserial modules. Recently, the authors introduced the classes of QTAG-modules namely as socle-regular and strongly socle-regular QTAG-modules which properly contain the classes of transitive and fully transitive QTAG-modules respectively. Here we define strongly and quasi transitivities and study the inter relations between various type of transitivities.
 Keywords
QTAG-module;Strongly;fully and weakly transitive module;
 Language
English
 Cited by
 References
1.
L. Fuchs, Infinite Abelian Groups, Vol. I, Academic Press, New York, (1970).

2.
L. Fuchs, Infinite Abelian Groups, Vol. II, Academic Press, New York, (1973).

3.
I. Kaplansky, Infinite Abelian Groups, University of Michigan Press, Ann Arbor. Mich., (1954).

4.
A. Mehdi, M. Y. Abbasi and F. Mehdi, Nice decomposition series and rich modules, South East Asian J. Math. & Math. Sci., 4(1), 1-6, (2005).

5.
A. Mehdi, S. A. R. K. Naji and A. Hasan, Small homomorphisms and large submodules of QTAG-modules, Scientia Series A., Math. Sci., 23(2012), 19-24.

6.
S. A. R. K. Naji, A study of different structures of QTAG-modules, Ph.D. Thesis, A.M.U., Aligarh, 2011.

7.
F. Sikander, A. Hasan and A. Mehdi, Socle-Regular QTAG-modules, New Trends in Math. Sci.,2(2) (2014), 129-133.

8.
F. Sikander, A. Hasan and F. Begum, On Strongly Socle-Regular QTAG-modules, Scientia Series A., Math. Sci., 25(2014), 47-53.

9.
S. Singh, Some decomposition theorems in abelian groups and their generalizations, Ring Theory, Proc. of Ohio Univ. Conf. Marcel Dekker N.Y. 25, 183-189, (1976).