Completely Semi Prime Ideal With Respect To An Element Of A Near Ring

Abstract

       In this paper ,we introduce the notions of completely semi prime ideal  with respect to an element x  (x-C.S.P.I)  of  a near ring  and  the completely semi prime ideal  near ring with respect to an element x (x-C.S.P.I ) .  1. The image and inverse image  of     x-C.S.P.I  under epimomorphism and the   2. direct product  of x-C.S.P.I  near ring are studied .