Abstract
In [4] Singh started the study of modules MR satisfying the following two conditions:
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(I)
Every finitely generated submodule of any homomorphic image of MR is a direct sum of uniserial modules.
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(II)
Given two uniserial submodules U and V of a homomorphic image of M, for any submodule W of U, any homomorphism f: W → V can be extended to a homomorphism g: U → V provided the composition length d(U/W) ≤ d(V/f(W)).
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References
K. Benabdallah and S. Singh, A note on Ulm’s theorem, Comm. Alg. (in press).
M.Z. Khan, Modules behaving like abelian groups, Can. Math. Bull., 22(1979) 449–457.
S. Singh, Modules over hereditary noetherian prime rings, Can. J. Math. 27 (1975) 867–883.
S. Singh, Some decomposition theorems in abelian groups and their generalizations, Proceedings of Ohio University Conference, Lecture Notes in Mathematics Vol. 25, 183–189, Marcel Dekker (1976).
S. Singh, Some decomposition theorems on abelian groups and their generalizations II, Osaka J. Math., 16 (1979) 45–55.
S. Singh and Wafa A. Ansari, On Ulm’s theorem, Comm. Algebra (in press).
M.H. Upham, Note on an extension of Ulm’s theorem, Comm. Algebra (in press).
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© 1983 Springer-Verlag Berlin Heidelberg
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Benabdallah, K., Singh, S. (1983). On Torsion Abelian Groups Like Modules. In: Göbel, R., Lady, L., Mader, A. (eds) Abelian Group Theory. Lecture Notes in Mathematics, vol 1006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21560-9_45
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DOI: https://doi.org/10.1007/978-3-662-21560-9_45
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