Congruences and isoton mappings of a partially ordered set
by
Sándor Radeleczki
Institute of Mathematics, University of Miskolc
Coauthors: Péter Körtesi, Szilvia Szilágyi

Our aim is to introduce a kind of "congruence notion" for partially ordered sets. A partition of a poset (P, <) is called order-preserving if < induces a partial order on the set of its blocks in a natural way. Order-preserving partitions of a a poset P can be characterized in several ways. They are the kernels of the isotone maps defined on P. They are exactly those partitions of P whose blocks are intervals of a linear extension of <. The order-preserving partitions of P form a complete lattice O(P) with respect to the partitions ordering. If P is finite, then O(P) is relatively complemented. If a poset P can be order-embedded in a direct product of some chains which are surjective isotone images of P, then this embedding is called subdirect. We characterize the subdirect embeddings of a poset P by the mean of the order-preserving partitions of P.

Date received: May 18, 2004