## Preprints (rote Reihe) des Fachbereich Mathematik

331

Strict order relations are defined as strict asymmetric and transitive binary relations. For classes of so-called levelled strict orders it is analyzed, under which conditions the endomorphism monoids of two relations coincide; in particular the case of direct sums of strict antichains is studied. Further, it is shown that these orders differ in their sets of binary order preserving functions.

332

In recent years a considerable attention was paid to an investigation of finite orders relative to different properties of their isotone functions [2,3]. Strict order relations are defined as strict asymmetric and transitive binary relations. Some algebraic properties of strict orders were already studied in [6]. For the class K of so-called 2-series strict orders we describe the partially ordered set EndK of endomorphism monoids, ordered by inclusion. It is obtained that EndK possesses a least element and in most cases defines a Boolean algebra. Moreover, every 2-series strict order is determined by its n-ary isotone functions for some natural number n.