Quasi-semiprime Modules

Abstract

    Suppose that A be an abelain ring with identity, B be a unitary (left) A-module, in this paper ,we introduce a type of modules ,namely Quasi-semiprime A-module, whenever   is a Prime Ideal For proper submodule N of  B,then B is called Quasi-semiprime module ,which is a Generalization of Quasi-Prime A-module,whenever  annAN is a prime ideal for proper submodule N of B,then B is Quasi-prime module .A comprchensive study of these modules is given,and we study the Relationship between quasi-semiprime module and quasi-prime .We put the codition coprime over cosemiprime ring for the two cocept quasi-prime module and quasi-semiprime module are equavelant.and the cocept of  prime module and quasi-semiprime module are equavelant.The codition of anti-hopfain make Quasi-Prime is Quasi-Semiprime A-module.Whenever B is Cyclic,Coprime C-Module,Where C be ring each ideal is semiprim,imlies Quasi-Prime,Quasi-SimePrime and annCB is Prime ideal are equaivelant.If F be eipemorphism from B1    B2 ,Whenever B1 is Quasi-SemiPrime Module,implies B2 is Quasi-semiprime A-Module and the iverse Image Of Quasi-Semiprime Is Quasi-SemiPrime A-Module.