Some specific classes of relations, a review


  • Daniel Abraham Romano


In this paper, the concepts of several new classes of relations on
sets are presented introduced by this author in the previous ve years. The following classes of relations have been introduced and partly described in several his articles: the class of quasi-regular, the class of quasi-conjugative, the class of quasi-normal and the class of normally conjugative relations.


[1] H.J.Bandelt. Regularity and complete distributivity. Semigroup Forum, 19(1980), 123-126.

[2] H.J.Bandelt. On regularity classes of binary relations. In: Universal Algebra and Applications. Banach Center Publications, vol. 9(1982), 329-333.

[3] G. Jiang and L. Xu. Conjugative relations and applications. Semigroup Forum, 80(1)(2010), 85-91.

[4] G. Jiang and L. Xu. Dually normal relations on sets. Semigrouop Forum, 85(1)(2012), 75-80.

[5] G. Jiang, L. Xu, J. Cai and G. Han. Normal Relations on Sets and Applications. Int. J. Contemp. Math. Sciences, 6(15)(2011), 721 - 726.

[6] J. M. Howie. An introduction to semigroup theory. Academic Press, 1976.

[7] M.Milovanovic and D.A.Romano. Neke nove relacije na skupovima. MAT-KOL, XVIII(2)(2012), 19-23.

[8] D.A.Romano. Quasi-conjugative relations on sets. MAT-KOL, XIX(3)(2013), 5-10.

[9] D.A.Romano. Quasi-regular relations A new class of relations on sets. Publ. de l'Inst. Math., 93(107)(2013), 127-132.

[10] D.A.Romano and M.Vincic. Finitelly quasi-conjugative relations. Bull. Int. Math. Virtual Inst., 3(1)(2013), 29-34.

[11] D.A.Romano. Jedna nova klasa relacija. MAT-KOL, XX(1)(2014), 5-14.

[12] D.A.Romano. Two new classes of relations. In: Mateljevic, Stanimirovic, Maric and Svetlik (Eds.) Symposium MATHEMATICS and APPLICATIONS, (24-25 May, 2013) (pp. 34-39), Faculty of Mathematics, University of Belgrade, Belgrade 2014.

[13] D.A.Romano. Bi-conjugative relations. Rom. J. Math. Com. Sci., 4(2)(2014), 203-208.

[14] D.A.Romano. Quasi-normal relations a new class of relations. Kyungpook Math. J., 55(3)(2015), 541-548.

[15] D.A.Romano. Finitely dual quasi-regular relations. Bull. Inter. Math. Virtual Inst., 5(2)(2015), 165-169.

[16] D.A.Romano. Finitely bi-conjugative relations. Rom. J. Math. Comp. Sci., 6(2)(2016), 134-138.

[17] D. A. Romano. Finitely dual quasi-normal relations. MAT-KOL, XXIII (1)(2017), 21-25.

[18] D.A.Romano. Normally conjugative relations. Asian-European J. Math., (AEJM), 10(2)(2017), ID: 1750036.

[19] B.M.Schein. Regular elements of the semigroup of all binary relations. Semigroup Forum, 13(1976), 95-102.

[20] M.Vincic and D.A.Romano. Finitely bi-quasiregular relations. Sarajevo J. Math., 10(22)(2014), 21-26.

[21] M.Vincic and D.A.Romano. Finitely bi-normal relations. Gulf J. Math., 3(3)(2015), 101-105.

[22] A. Zareckii. The semigroup of binary relations. Mat. Sbornik, 61(3)(1963), 291-305 (In Russian)

[23] X.-Q. Xu and Y.M. Liu. Relational representations of hypercontinuous lattices. In: Domain Theory, Logic, and Computation (pp. 65{74), Kluwer, Dordrecht, 2003.





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