The structure of finite 0,1-posets (Q1069962)

A finite poset with a least element and a greatest element is called a 0,1-poset. \textit{K. Leutola} and \textit{J. Nieminen} [Algebra Univers. 16, 344-354 (1983; Zbl 0514.06003)] have shown that for any finite 0,1-poset \(P_{01}\) one can construct algebras, called \(\chi\)-lattices, which determine the order structure of \(P_{01}\). This paper studies the structure of finite 0,1-posets by means of \(\chi\)-lattices of \(P_{01}\), graphs and of closed substructures of \(P_{01}\). The structural properties found for 0,1-posets are generalizations of analogous properties of lattices. Semimodularity, strong semimodularity, modularity and distributivity in 0,1-posets are described.