III-homomorphisms and III-congruences on posets
In the paper a new kind of homomorphism (III-homomorphism) between partially ordered sets is introduced and investigated. The authors study some properties of these homomorphisms, the corresponding congruences and their relationship to the other known homomorphisms, namely isotone mappings, strong homomorphisms, \(w\)-stable strong homomorphisms and \(LU\)-morphisms. III-homomorphisms turn out to be intermediate between strong homomorphisms and \(w\)-stable strong homomorphisms [\textit{R. Halaš}, ``Congruences on posets'', in: D. Dorninger et al. (eds.), Contributions to general algebra 12. Proceedings of the 58th workshop on general algebra ``58. Arbeitstagung Allgemeine Algebra'', Vienna, Austria, June 3--6, 1999. Klagenfurt: Verlag Johannes Heyn. 195--210 (2000; Zbl 0965.06001)]. The paper presents an approach which in some sense completes the hierarchy of definitions used so far.
scientific article; zbMATH DE number 5349300
scientific article