A NOTE ON COMPLETELY SEMI-PRIME IDEALS IN NEAR-RINGS

Abstract

The aim of the present paper is to prove that (i)  Every completely semi-prime ideal I of N is the intersection of all completely prime ideals of I;  and  (ii) If I is a completely semi-prime ideal of N, then an ideal P of N is a minimal completely prime ideal of I if and only if  P is a minimal prime ideal of I,  where N is a zero-symmetric near-ring.  We also discussed the relations between the prime radical and completely prime radical.  In particular, we proved that these two radicals are equal in case of a particular type of near-rings called PC near-rings.  Related examples were presented whenever necessary. 

A.M.S. Subject Classification:  16 D 25, 16 Y 30, and 16 Y 99.