Prime z

چکیده مقاله

Let I and J be ideals of a commutative ring R. we call I a z-ideal, if Ma I; for all a 2 I, where Ma is the intersection of all maximal ideals containing a. The aim of this paper is generalize the notion of z-ideals and zJ -ideals to noncommutative rings. If I be a z-ideal in a right duo ring and P 2 Min(I), we will present a condition which P is a z-ideal. Also we will prove that if I is a left zJ -ideal of a P- right duo ring and P 2 Min(I), then P is a left zJ -ideal. Finally, we show that whenever P and Q are prime ideals of a P- right duo ring R which are not comparable and P Q is a left zJ -ideal of R, then both P and Q are left zJ -ideals.