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Characterizations of commuting relations. (English) Zbl 1116.08001
Summary: We give some necessary and sufficient conditions for two preorders, tolerances, resp. equivalences \(R\) and \(S\) on the same set to commute with respect to composition.

08A02 Relational systems, laws of composition
03E20 Other classical set theory (including functions, relations, and set algebra)
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[1] T. Glavosits: Generated preorders and equivalences. Acta Acad. Paed. Agriensis, Sect. Math. 29 (2002), 95-103. · Zbl 1012.08002
[2] T. Glavosits: Preorders and equivalences generated by, commuting relations. Acta Math. Acad. Paedagog. Nyhazi. (N.S.) 18 (2002), 53-56) · Zbl 1012.08003
[3] T. Glavosits, Á. Száz: Decompositions of commuting relations. Acta Math. Inform. Univ. Ostrava 11 (2003), 25-28. · Zbl 1182.08001
[4] O. Ore: Theory of equivalence relations. Duke Math. J. 9 (1942), 573-627. · Zbl 0060.06201
[5] G. Pataki, Á. Száz: A unified treatment of well-chainedness and connectedness, properties. Acta Math. Acad. Paedagog. Nyhazi. (N.S.) 19 (2003), 101-165) · Zbl 1049.54023
[6] F. Šik: Über Charakterisierung kommutativer. Zerlegungen Spisy vyd. přírod. fak. Masarykovy univ. 1954/3 , 97-102. · Zbl 0059.02101
[7] A. Száz: Relations bibitemining and dividing each other. Pure Math. Appl. 6 (1995), 385-394. · Zbl 0942.54016
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