Geodesic
Congruences in ordered sets and LU compatible equivalences
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 48 (2009) no. 1, pp. 153-156 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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A concept of equivalence 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.
A concept of equivalence 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.
Classification : 06A06, 06B10
Keywords: Ordered set; morphism; $LU$ compatible equivalence 
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Snášel, Václav; Jukl, Marek. Congruences in ordered sets and LU compatible equivalences. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 48 (2009) no. 1, pp. 153-156. http://geodesic.mathdoc.fr/item/AUPO_2009_48_1_a12/

[1] Chajda, I., Snášel, V.: Congruences in ordered sets. Math. Bohem. 123, 1 (1998), 95–100. | MR

[2] Kolibiar, M.: Congruence relations and direct decomposition of ordered sets. Acta Sci. Math. (Szeged) 51 (1987), 129–135. | MR

[3] Kolibiar, M.: Congruence relations and direct decomposition of ordered sets II. Contributions to General Algebra 6 (1988), 167–171. | MR

[4] Haviar, A., Lihová, J.: Varieties of posets. Order 22, 4 (2005), 343–356. | MR | Zbl

[5] Halaš, R.: Congruences on posets. Contributions to General Algebra 12 (2000), 195–210. | MR

[6] Halaš, R., Hort, D.: A characterization of 1,2,3,4-endomorphisms of posets. Czech. Math. J. 53, 128 (2003), 213–221. | MR