Preimero

sfjhf sadfjlksdf lksdjfl saldkfjlsd

kdkdkdk

In this paper, we first study the relations between semiprime ideals and ideals of the ideal lattice of posets. Moreover, we study the relation between prime ideals of a poset P and prime ideals of the set Id(P) of all ideals of P. We extend separation theorem for semiprime to a finite up directed poset with some constraint on the filter and for prime ideals to the case of finite poset. Then we prove the prime separation theorem for finite posets P for which Id(P) is distributive.