On strongly ⊕-supplemented modules
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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.
KeywordsDirect Summand Left Ideal Projective Module Projective Cover Discrete Valuation Ring
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