Foundations of Neutrosophic N-Semirings Theory and Structural Properties

In this paper the concept of neutrosophic n-semirings (S∪ I, ∗ 1, ∗ 2, ∗ 3,..., ∗ n, ∗ n+1) has been introduced. The substructure of n-semirings (S∪ I, ∗ 1, ∗ 2, ∗ 3,..., ∗ n, ∗ n+1) has been defined and some useful results have been proved. Moreover, in order to familiarize the readers with these concepts some worthy examples have been coined. The left, right and two sided ideals of neutrosophic n-semirings have been paid a special heed. Finally we have turned our discussion towards the compatible and congruence relations and some remarkable properties have also been considered. Furthermore, we vividly have given examples to express the rationality of each notion popularized in this paper.