Title of article :
Z-prime gamma submodule of gamma modules
Author/Authors :
Alhussein Zyarah, Ali Abd Iraqi Ministry of Education - General Directorate of Education for the Holy Karbala, Karbala, Iraq , Hussain, Ahmad Hadi Department of Energy Engineering - College of Engineering Al-musayab - University of Babylon, Babil, Iraq , Kadhim Zghair, Hayder Department of Software - Information Technology College - University of Babylon, Iraq
Abstract :
Let R be a Γ-ring and ∂ be an RΓ-module. A proper RΓ-submodule. T of an RΓ-module ∂ is called Z-prime RΓ-submodule if for each t∈∂,γ∈Γ and f∈∂∗=HomRΓ(∂,R),f(t)γt∈T implies that either t∈T or f(t)∈[T:RΓ ∂]. The purpose of this paper is to introduce interesting theorems and properties of Z- prime RΓ-submodule of RΓ-module and the relation of Z-prime RΓ-submodule, which represents of generalization Z-prime R-submodule of R-module.
Keywords :
Gamma-ring , RGamma-module , RGamma-submodule , and prime RGamma -submodule
Journal title :
International Journal of Nonlinear Analysis and Applications
