Some results of semi-prime ideal of the ring

By discussing the property of semi prime ideals and obtaining the follow results of representing semi prime ideal by prime ideals:(1) ideal Q of the ring R be semi prime ideal if and only if Q can be written as intersection of some prime ideals;(2) for any semi prime ideal Q and x∈R-Q,there exist prime ideal P such that xPQ;(3) every semi prime ideal of Artin ring R can be written as finite intersection of minimal prime ideals and the represent is unique.