2-Absorbing R-ideals of modules over near rings

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.