Pseudo Symmetric Ideals and Pseudo Symmetric Near-rings.

In this paper, we first introduce the notions of pseudo symmetric subset and pseudo symmetric ideal of a near-ring and define pseudo symmetric near-ring. We prove that every completely prime (resp. completely semiprime) ideal of a near-ring is a pseudo symmetric ideal. We also show that a near-ring satisfying the strong insertion factor property (resp. the weak commutative near-ring ) is a pseudo sym- metric near-ring. Moreover, we investigate the relations among the radicals of type 1 prime, pseudo symmetric, completely prime, com- pletely semiprime, primary and semiprimary ideals of a near-ring [ABSTRACT FROM AUTHOR]