Abstract:
It is known that near rings and modules over near rings are generalized algebraic structures of rings and modules over rings, respectively. In this thesis, we introduce the concepts of 2-absorbing R-ideals of modules over near rings and 2-absorbing ideals of near rings which are generalization of prime R-ideals of modules over near rings and prime ideals of near rings, respectively. Moreover, we present some results analogous to those in ring theory. We provide the notions of strongly 2- absorbing R-ideals of modules over near rings and strongly 2-absorbing ideals of near rings and study some of their properties. Finally, we also focus on some results of 2-absorbing R-ideals of modules over decomposable near rings and 2-absorbing ideals of decomposable near rings.
