Quasi-semiprime Modules

Main Article Content

Muntaha Abdul- Razaq Hasan

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.

Article Details

How to Cite
[1]
Abdul- Razaq Hasan, M. 2023. Quasi-semiprime Modules. Ibn AL-Haitham Journal For Pure and Applied Sciences. 36, 4 (Oct. 2023), 377–383. DOI:https://doi.org/10.30526/36.4.3181.
Section
Mathematics

Publication Dates

References

AL-Bahraany,B.Anote on prime modules and pure submodules,J.sclence 1996,37,2,1431-1441.

Desale,G.;, Nicholson,W.K.,Endoprimitive Ring ,J.Algebra 1981,70,3,548-560. DOI: https://doi.org/10.1016/0021-8693(81)90235-0

Hasan,M.A.Quasi-prime module and Quasi prime submodule,M.SC..Thesis 1999,Univ.of Babhdad.

Hirano,Y. ;Mogani,I.On Restricted Anti-Hopfinan Modules,Math.J.,Kayama1986 ,Univ.,.28,119-131.

.AL-Awadi, H.K.Anti-Hopfian Modules and Restricted Anti-Hopfian,M.SC.,thesis 200,Univ. of Baghdad.

Hadi.M.A.I,;Kassm,I.R.,Coprime Modules And Other Related Topics,,Journal of physics 2018 1003,1,1-15. DOI: https://doi.org/10.1088/1742-6596/1003/1/012043

Hadi M.A.I ;Kasam,.I.R. Dual Notations of Prime Modules,Ibn AL.Haitham J. for pure and ppl.sci.,2010, 23,.3.

Szasz F.A,Radicals of Rings,Budapest,Hungary,chichester and Akademiai Kiado,1981,PP.139.

Annin,S.,Associated and Attached primes over Non commutative Rings ,Ph.D.Thesis 2002,Univ.of Berkeley.