On some properties of \(\oplus\)-supplemented modules.
Summary: A module \(M\) is \(\oplus\)-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 \(\oplus\)-supplemented module is not in general \(\oplus\)-supplemented. We prove that over a commutative ring \(R\), every finitely generated \(\oplus\)-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 \(\oplus\)-supplemented \(R\)-modules coincides with the class of injective \(R\)-modules. The structure of \(\oplus\)-supplemented modules over a commutative principal ideal ring is completely determined.
scientific article; zbMATH DE number 2166339