THE STUDY OF Z-IDEALS WHICH ARE RIGHT PRIMARY IDEALS

In this note, we study the z-ideals which are right primary ideals in right duo rings. Using the connection between z-ideals and right primary ideals, it is proved that every ideal of a semisimple right duo ring is a finite intersection of prime z-ideals. If I is a right primary ideal, we give conditions that the intersection of z-ideals containing I, is a prime z-ideal. Finally, we see that if I is a z-ideal of a right duo ring, then I is a right primary ideal if and only if I is a left primary ideal.