Year 2014,
Volume: 2 Issue: 2, 129 - 133, 01.08.2014
Abstract
A right module over an associative ring with unity is a -module if every finitely generated submodule of any homomorphic image of is a direct sum of uniserial modules. In this paper we focus our attention to the socles of fully invariant submodules and introduce a new class of modules, which we term socle-regular -modules. This class is shown to be large and strictly contains the class of fully transitive modules. Also, here we investigated some basic properties of such modules
References
- Fuchs L., Infinite Abelian Groups, Vol. I, Academic Press, New York, (1970).
- Fuchs L., Infinite Abelian Groups, Vol. II, Academic Press, New York, (1973).
- Hefzi M. A. and Singh S., On σ-pure submodules of QTAG-modules, Arch. Math., 46(1986), 501 − 510.
- Kaplansky I., Infinite Abelian Groups, University of Michigan Press, Ann Arbor, 1954 and 1969.
- Khan, M.Z., Modules behaving like torsion abelian groups II, Math. Japonica, 23(5)(1979), 509 − 516.
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- Mehdi A., Abbasi M. Y. and Mehdi F., On (ω + n)-projective modules, Ganita Sandesh, 20(1), 27-32, (2006).
- Mehdi A., Naji S.A.R.K and Hasan A., Small homomorphisms and large submodules of QTAG-modules, Scientia Series A., Math. Sci., 23(2012), 19-24.
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Year 2014,
Volume: 2 Issue: 2, 129 - 133, 01.08.2014
Abstract
References
- Fuchs L., Infinite Abelian Groups, Vol. I, Academic Press, New York, (1970).
- Fuchs L., Infinite Abelian Groups, Vol. II, Academic Press, New York, (1973).
- Hefzi M. A. and Singh S., On σ-pure submodules of QTAG-modules, Arch. Math., 46(1986), 501 − 510.
- Kaplansky I., Infinite Abelian Groups, University of Michigan Press, Ann Arbor, 1954 and 1969.
- Khan, M.Z., Modules behaving like torsion abelian groups II, Math. Japonica, 23(5)(1979), 509 − 516.
- Mehdi A., Abbasi M. Y. and Mehdi F., Nice decomposition series and rich modules, South East Asian J. Math. & Math. Sci., 4(1), 1- 6, (2005).
- Mehdi A., Abbasi M. Y. and Mehdi F., On (ω + n)-projective modules, Ganita Sandesh, 20(1), 27-32, (2006).
- Mehdi A., Naji S.A.R.K and Hasan A., Small homomorphisms and large submodules of QTAG-modules, Scientia Series A., Math. Sci., 23(2012), 19-24.
- Singh S., Some decomposition theorems in abelian groups and their generalizations, Ring Theory, Proc. of Ohio Univ. Conf. Marcel Dekker N.Y. 25, 183-189, (1976).
There are 9 citations in total.
Details
| Journal Section | Articles |
|---|---|
| Authors | |
| Publication Date | August 1, 2014 |
| Published in Issue | Year 2014 Volume: 2 Issue: 2 |