Local methods for Rosenberg relations (Q992013)

For six kinds of so-called Rosenberg relations \(r\) on a finite set \(A\), e.g. equivalence relations, the author develops uniform decision procedures for the problem whether, given any other relation \(s\) on \(A\), every unary operation on \(A\) compatible with \(r\) (alias \(r\)-endomorphism) is also compatible with \(s\). The use of local methods à la \textit{M. Ponjavić} [in: I. Chajda et al. (eds.), Proceedings of the 68th workshop on general algebra ``68. Arbeitstagung Allgemeine Algebra'', Dresden, Germany, June 10--13, 2004 and of the summer school 2004 on general algebra and ordered sets, Malá Morávka, Czech Republic, September 5--11, 2004. Klagenfurt: Verlag Johannes Heyn. Contributions to General Algebra 16, 189--197 (2005; Zbl 1083.08002)], which are essential for the decision procedures, is also illustrated by the enumeration of all relations in the ternary part of the weak Krasner algebra of the three-element chain.