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Quotients and homomorphisms of relational systems. (English) Zbl 1241.08001

Relational systems with one binary operation in the sense of J. Riguet [Bull. Soc. Math. Fr. 76, 114–154 (1948; Zbl 0033.00603)] are investigated in the paper. First, an algebraic approach of A. I. Mal’tsev [Algebraic systems. Berlin-Heidelberg-New York: Springer-Verlag; Berlin: Akademie-Verlag (1973; Zbl 0266.08001)] is applied to quotient relational systems, homomorphisms, strong mappings and cone-preserving mappings. Then the connection between directed relational systems and some groupoids is studied.

MSC:

08A02 Relational systems, laws of composition
20N02 Sets with a single binary operation (groupoids)
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References:

[1] Chajda, I.: Congruences in transitive relational systems. Miskolc Math. Notes 5 (2004), 19-23. · Zbl 1047.08001
[2] Chajda, I.: Class preserving mappings of equivalence systems. Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica 43 (2004), 61-64. · Zbl 1077.08001
[3] Chajda, I.: Homomorphisms of directed posets. Asian-European J. Math. 1 (2008), 45-51. · Zbl 1159.06002
[4] Chajda, I., Hošková, Š.: A characterization of cone preserving mappings of quasiordered sets. Miskolc Math. Notes 6 (2005), 147-152. · Zbl 1095.08001
[5] Mal’cev, A. I.: Algebraic Systems. Springer, New York, 1973.
[6] Riguet, J.: Relations binaires, fermetures, correspondances de Galois. Bull. Soc. Math. France 76 (1948), 114-155. · Zbl 0033.00603
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