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Chajda, Ivan ; Snášel, Václav
Congruences in ordered sets. (English). Mathematica Bohemica, vol. 123 (1998), issue 1, pp. 95-100
MSC: 06A06, 06B10 | MR 1618652 | Zbl 0897.06004 | DOI: 10.21136/MB.1998.126291
Keywords:
congruence preserving upper and lower bounds; morphism; lattice congruence; poset; ordered set; lower and upper bounds
Summary:
A concept of congruence preserving upper and lower bounds in a poset $P$ is introduced. If $P$ is a lattice, this concept coincides with the notion of lattice congruence.
References:
[Dor] G. Dorfer: Sublattice-extensions by means of convex sublattices. Contributions to General Algebra 9. Verlag Hölder-Pichler-Temski, Wien, 1995, pp. 127-132. MR 1484432
[GR] G. Grätzer: General Lattice Theory. Birkhäuser, Basel-Stuttgart, 1987.
[Kol] M. Kolibiar: Congruence relations and direct decomposition of ordered sets. Acta Sci. Math. (Szeged) 51 (1987), 129-135. MR 0911564
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