Homomorphisms of directed posets. (English) Zbl 1159.06002

In the paper homomorphisms and congruences of directed posets are investigated. The concept of homomorphism modifies the notion of III-homomorphism introduced and studied by K. P. Shum, P. Zhu and N. Kehayopulu [Discrete Math. 308, No. 21, 5006–5013 (2008; Zbl 1148.06001)]. The author’s approach relies on the fact that every directed poset can be converted into a so-called commutative directoid, an algebra with one binary operation. Poset homomorphisms are naturally chosen to be just homomorphisms of the corresponding directoids.


06A06 Partial orders, general
06A12 Semilattices
06B10 Lattice ideals, congruence relations


Zbl 1148.06001
Full Text: DOI


[1] Chajda I., Math. Bohem. 123 pp 95–
[2] DOI: 10.1023/A:1022944013075 · Zbl 1015.06002
[3] DOI: 10.1007/BF01190253 · Zbl 0699.08002
[4] Kolibiar M., Acta Sci. Math. (Szeged) 51 pp 129–
[5] Körtesi P., Math. Panonica 16 pp 39–
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