On \(H\)-cofinitely supplemented modules. (Q459201)

The authors study \(H\)-cofinitely supplemented modules, defined as follows. A module \(M\) is called \(H\)-cofinitely supplemented if for every submodule \(E\) of \(M\) such that \(M/E\) is finitely generated there exists a direct summand \(D\) of \(M\) such that \(M=E+X\) holds if and only if \(M=D+X\) for every submodule \(X\) of \(M\). Among other properties, they show that if \(M=M_1\oplus M_2\) is a direct sum of \(H\)-cofinitely supplemented modules such that \(M_1\) is radical \(M_2\)-projective, then \(M\) is \(H\)-cofinitely supplemented. Rings whose modules are \(H\)-cofinitely supplemented are also studied.