On some properties of -supplemented modules

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.