On Centrally Prime and Centrally Semiprime Rings

In this paper, centrally prime and centrally semiprime rings are defined and the relations between these two rings and prime (resp. semiprime) rings are studied.Among the results of the paper some conditions are given under which prime (resp. semiprime) rings become centrally prime (resp.centrally semiprime) as in:1-A nonzero prime (resp. semiprime) ring which has no proper zero divisors is centrally prime (resp.centrally semiprime).Also we gave some other conditions which make prime (resp. semiprime) rings and centrally prime (resp.centrally semiprime) rings equivalent, as in :2-A ring which satisfies the-for multiplicative systems is prime (resp. semiprime) if and only if it is centrally prime (resp.centrally semiprime).3-A ring with identity in which every nonzero element of its center is a unit is prime (resp. semiprime) if and only if it is centrally prime (resp.centrally semiprime).