Imbeddedness and direct sum of uniserial modules
DOI:
https://doi.org/10.5269/bspm.62192Resumen
In this paper, we study a generalization of $h$-pure submodules as well as some other closely related concepts. Here, we examine the extent of this generalization in several ways. We then use this to give a characterization of the imbedded-complete modules. It is found that imbeddedness can considerably more abundant than $h$-purity on direct sum of uniserial modules.
Referencias
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4. Hasan A., On quasi-large submodules of QTAG-modules, Asian-Europen J. Math., 9(2), 1650033(1-8), (2016).
5. Hasan A., Subsocles and direct sum of uniserial modules, J. Algebra Comb. Discrete Appl., 8(3), 213-218, (2021).
6. Keane W. J., Imbedded N-high subgroups of abelian groups, Comment. Math. Univ. St. Pauli, 29(2), 145-155, (1980).
7. Keane W. J., On minimal imbedded subgroups of abelian p-groups, Comment. Math. Univ. St. Pauli, 31(2), 155-158, (1982).
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9. Khan M. Z., Ahmad M. and Ansari A.H., On subsocles of S2-modules-II, Kyungpook Math. J., 31(2), 207-217, (1991).
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11. Mehdi A. and Mehdi F., N-high submodules and h-topology, South East Asian J. Math & Math Sci, 1(1), 83–85, (2002).
12. Mehdi A., Naji S.A.R.K. and Hasan A., Small homomorphisms and large submodules of QTAG-modules, Sci. Ser. A. Math Sci., 23, 19-24, (2012).
13. Mehran H. A. and Singh S., On σ-pure submodules of QTAG-modules, Arch. Math., 46(6), 501-510, (1986).
14. Singh S., Some decomposition theorems in abelian groups and their generalizations, Ring Theory: Proceedings of Ohio University Conference, Marcel Dekker, New York 25, 183-189, (1976).
15. Singh S., Abelian groups like modules, Act. Math. Hung, 50, 85-95, (1987).
2. Fuchs L., Infinite Abelian Groups, Volume I, Pure Appl. Math. 36, Academic Press, New York, 1970.
3. Fuchs L., Infinite Abelian Groups, Volume II, Pure Appl. Math. 36, Academic Press, New York, 1973.
4. Hasan A., On quasi-large submodules of QTAG-modules, Asian-Europen J. Math., 9(2), 1650033(1-8), (2016).
5. Hasan A., Subsocles and direct sum of uniserial modules, J. Algebra Comb. Discrete Appl., 8(3), 213-218, (2021).
6. Keane W. J., Imbedded N-high subgroups of abelian groups, Comment. Math. Univ. St. Pauli, 29(2), 145-155, (1980).
7. Keane W. J., On minimal imbedded subgroups of abelian p-groups, Comment. Math. Univ. St. Pauli, 31(2), 155-158, (1982).
8. Khan M. Z., On h-purity in QT AG-modules, Comm. Algebra, 16(12), 2649-2660, (1988).
9. Khan M. Z., Ahmad M. and Ansari A.H., On subsocles of S2-modules-II, Kyungpook Math. J., 31(2), 207-217, (1991).
10. Khan M. Z. and Rafiquddin, Imbedded submodules, Aligarh Bull. Math., 16, 1-8, (1995).
11. Mehdi A. and Mehdi F., N-high submodules and h-topology, South East Asian J. Math & Math Sci, 1(1), 83–85, (2002).
12. Mehdi A., Naji S.A.R.K. and Hasan A., Small homomorphisms and large submodules of QTAG-modules, Sci. Ser. A. Math Sci., 23, 19-24, (2012).
13. Mehran H. A. and Singh S., On σ-pure submodules of QTAG-modules, Arch. Math., 46(6), 501-510, (1986).
14. Singh S., Some decomposition theorems in abelian groups and their generalizations, Ring Theory: Proceedings of Ohio University Conference, Marcel Dekker, New York 25, 183-189, (1976).
15. Singh S., Abelian groups like modules, Act. Math. Hung, 50, 85-95, (1987).
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2024-04-19
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