Abstract. In this paper, we prove that a bounded poset $P$ is a pseudocomplemented poset satisfying the Stone identity if the set of all semicomplements of every element of $P$ forms an $u$-ideal which is a dual modular direct factor of $P$. Further, we prove that a bounded pseudocomplemented poset $P$ in which every normal ideal is principal satisfies the Stone identity if and only if $Id(P)$ also satisfies the Stone identity.

AMS Subject Classification (1991): 06C15, 06A12

Keyword(s): Stone poset, dual modular poset, pseudocomplemented poset

Received June 3, 2011, and in final form September 2, 2011. (Registered under 28/2011.)