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On some properties of ⊕ -supplemented modules

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  • A. Idelhadj
  • R. Tribak

Abstract

A module M is ⊕ -supplemented if every submodule of M has a supplement which is a direct summand of M . In this paper, we show that a quotient of a ⊕ -supplemented module is not in general ⊕ -supplemented. We prove that over a commutative ring R , every finitely generated ⊕ -supplemented R -module M having dual Goldie dimension less than or equal to three is a direct sum of local modules. It is also shown that a ring R is semisimple if and only if the class of ⊕ -supplemented R -modules coincides with the class of injective R -modules. The structure of ⊕ -supplemented modules over a commutative principal ideal ring is completely determined.

Suggested Citation

  • A. Idelhadj & R. Tribak, 2003. "On some properties of ⊕ -supplemented modules," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-15, January.
    • Handle: RePEc:hin:jijmms:291484
    DOI: 10.1155/S016117120320346X
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