  We study ideals and filters of posets and of pseudocomplemented posets and
show a version of the Separation Theorem, known for ideals and filters in
lattices and semilattices, within this general setting. We extend the concept
of a *-ideal already introduced by Rao for pseudocomplemented distributive
lattices and by Talukder, Chakraborty and Begum for pseudocomplemented
semilattices to pseudocomplemented posets. We derive several important
properties of such ideals. Especially, we explain connections between prime
filters, ultrafilters, filters satisfying the *-condition and dense elements.
Finally, we prove a Separation Theorem for *-ideals.
