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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.

MSC:

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

Citations:

Zbl 1148.06001
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References:

[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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