Semiprime RÎ“-Submodules of Multiplication RÎ“-Modules

Ali Abd Alhussein  Zyarah; Nuhad Salim  Al-Mothafar

doi:10.24996/ijs.2020.61.5.19

Authors

Ali Abd Alhussein Zyarah Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq
Nuhad Salim Al-Mothafar Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq

DOI:

https://doi.org/10.24996/ijs.2020.61.5.19

Keywords:

Î“ â€“ ring, RÎ“-module, RÎ“-submodule, prime RÎ“-submodule

Abstract

Let R be a Î“-ring and G be an R_Î“-module. A proper R_Î“-submodule S of G is said to be semiprime R_Î“-submodule if for any ideal I of a Î“-ring R and for any R_Î“-submodule A of G such that or which implies that . The purpose of this paper is to introduce interesting results of semiprime R_Î“-submodule of R_Î“-module which represents a generalization of semiprime submodules.