  In their recent paper on posets with a pseudocomplementation denoted by * the
first and the third author introduced the concept of a *-ideal. This concept is
in fact an extension of a similar concept introduced in distributive
pseudocomplemented lattices and semilattices by several authors, see
References. Now we apply this concept of a c-ideal (dually, c-filter) to
complemented posets where the complementation need neither be antitone nor an
involution, but still satisfies some weak conditions. We show when an ideal or
filter in such a poset is a c-ideal or c-filter, respectively, and we prove
basic properties of them. Finally, we prove so-called Separation Theorems for
c-ideals. The text is illustrated by several examples.
