On strongly -supplemented modules - Nebiyev, C.; Pancar, A. (Ukrains’kyi Matematychnyi Zhurnal, 2011)
In this work, strongly -supplemented and strongly cofinitely -supplemented modules are defined and some properties of strongly -supplemented and strongly cofinitely -supplemented modules are investigated. Let R be a ring. Then every R-module is strongly -supplemented if and only if R is perfect. Finite direct sum of -supplemented modules is -supplemented. But this is not true for strongly -supplemented modules. Any direct sum of cofinitely -supplemented modules is cofinitely -supplemented but this is not true for strongly cofinitely -supplemented modules. We also prove that a supplemented module is strongly -supplemented if and only if every supplement submodule lies above a direct summand.