الخلاصة

In this paper, we introduce the notions of primary ideal with respect to an element x denoted by (x- Pr.I) of a near ring and the primary ideals near ring with respect to an element x. Also, we study the image, inverse image of x- Pr.I under epimomorphism, the direct product of x-Pr.I near rings, and some types of ideals that becomes (x- Pr.I) of a near ring,and the Relationships among the primary ideal with respect to an element x of a near ring and some other types of ideals.