+-g-radical supplemented modules

Let M be an R-module. If every submodule of M has a g-radikal supplement that is a direct summand of M, then M is called a +-g-radical supplemented module. Let M be a g-radical supplemented module. If every g-radical supplement submodule in M is a direct summand of M, then M is called a strongly +-g-radical supplemented module. In this thesis work, these modules are investigated and some results of these modules are obtained. In this thesis work, all modules are unital modules on ring with identity. In this work, it is proved that the finite direct sum of +-g-radical supplemented modules is also +-g-radical supplemented. Let M be a +-g-radical supplemented and duo module. It is proved that every factor module of M and every homomorphic image of M are also +-g-radical supplemented. It is also proved that every direct summand of M is strongly +-g-radical supplemented, where M is a strongly +-g-radical supplemented module. Let M be a distributive and +-g-radical supplemented module. In this case, every factor module and every homomorphic image of M are also +-g-radical supplemented. Let M be a +-g-radical supplemented module with (D3) property. In this case, every direct summand of M is also +-g-radical supplemented. Let M be a +-g-radical supplemented R-module with (D3) property and f : M→N be an R-module epimorphism with N is an R-module. If Ker(f) is a direct summand of M, then N is also +-g-radical supplemented. Let M be a +-g-radical supplemented R-module with SSP property. In this case, M/K is also +-g-radical supplemented for every direct summand K of M. Let M be a g-supplemented module. If every g-supplement submodule in M is a direct summand of M, then M is called a strongly +-g-supplemented module. Let M be a strongly +-g-radical supplemented R-module. If RadgM<