Characterizations of the 0-distributive poset

Balasubramani and Venkatanarasimhan [1] characterized 0-distributive lattices in terms of semiideals, ideals and filters. Balasubramani [2] extends some of the characterizations of the 0-distributive lattices to 0-distributive semilattices. This paper extends some of the characterizations of the 0-distributive lattices and 0-distributive semilattices to 0-distributive posets. Some sufficient conditions and some necessary conditions for 0-distributivity are obtained. Counter examples are given to prove that certain conditions are not necessary and certain conditions are not sufficient.