On some properties of ⊕ -supplemented modules

A. Idelhadj and R. Tribak

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-15

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.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:291484

DOI: 10.1155/S016117120320346X

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