Strongly ⊕-supplemented and strongly cofinitely ⊕-supplemented modules are defined and some properties of strongly ⊕-supplemented and strongly cofinitely ⊕-supplemented modules are investigated. Let R be a ring. Then every R-module is strongly ⊕-supplemented if and only if R is perfect. The finite direct sum of ⊕-supplemented modules is ⊕-supplemented. However, this is not true for strongly ⊕-supplemented modules. Any direct sum of cofinitely ⊕-supplemented modules is cofinitely ⊕-supplemented but this is not true for strongly cofinitely ⊕-supplemented modules. We also prove that a supplemented module is strongly ⊕-supplemented if and only if every supplement submodule lies above a direct summand.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 5, pp. 662–667, May, 2011.
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Nebiyev, C., Pancar, A. On strongly ⊕-supplemented modules. Ukr Math J 63, 768–775 (2011). https://doi.org/10.1007/s11253-011-0541-9
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DOI: https://doi.org/10.1007/s11253-011-0541-9