On near generalized rings

Near ring is a generalization of ring: addition need not be abelian, and (more importantly) only one distributive law is postulated. In this paper, we establish a new generalization of near ring, namely near generalized ring. We also investigate some interesting algebraic properties of the near generalized ring. Moreover, we discuss the concept of commutativities and homomorphisms of near generalized rings and then some related properties are investigated. Furthermore, we introduce the notion of quotient structures of near generalized rings using congruence relations. Finally, fundamental theorem of near generalized ring homomorphisms analogues of ring theory is obtained.