On Fully Semiprime Submodules and Fully Semiprime Modules - Hadi, I.M.A.; Shihab, B.N. (Ibn AL-Haitham Journal For Pure and Applied Sciences, 2017)
Let R be a commutative ring with unity and let M be a unitary R-module. In this paper we study fully semiprime submodules and fully semiprime modules, where a proper fully invariant R-submodule W of M is called fully semiprime in M if whenever Xï€ªXïƒW for all fully invariant R-submodule X of M, implies XïƒW.         M is called fully semiprime if (0) is a fully semiprime submodule of M. We give basic properties of these concepts. Also we study the relationships between fully semiprime submodules (modules) and other related submodules (modules) respectively.