On 3-semiprime Ideal With Respect To An element Of A near ring

Abstract

In this paper ,we introduce the notions 3-semiprime ideal with respect to an element x denoted by  (x-3-S-P-I )  of a near ring  and  the 3-semiprime ideal  near ring with respect to an element x denoted by  (x-3-S-P-I near ring  ),and we studied the image and inverse image of x-3-S-P-I under epimomorphism and the direct product of  x-3-S-P-I  of near ring and we extension to fuzzify this notions and give some properties and examples about this .