Title of article :
On Fully Semiprime Submodules and Fully Semiprime Modules
Author/Authors :
Hadi, I.M.A. University of Baghdad - Ibn-Al-Haitham, College of Education - Department of Mathematics, Iraq , Shihab, B.N. University of Baghdad - Ibn-Al-Haitham, College of Education - Department of Mathematics, Iraq
Abstract :
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 XXW for all fully invariant R-submodule X of M , implies XW. 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
Keywords :
Fully semiprime submodule , fully semiprime modules , fully invariant submodule , fully prime modules
Journal title :
Ibn Alhaitham Journal For Pure and Applied Science
Journal title :
Ibn Alhaitham Journal For Pure and Applied Science
