This article is cited in 6 papers

The endotopism semigroups of an equivalence relation

Yu. V. Zhuchok^a, E. A. Toichkina<sup>b

a</sup> National Taras Shevchenko University of Kyiv
^b Lugansk Taras Shevchenko National University

Abstract: In this work we investigate six types of endotopism semigroups for a given equivalence relation. Necessary and sufficient conditions for the existence of all such endotopisms are presented. Conditions for the regularity and coregularity of each of the endotopism semigroups of a given type are established. The notion of the endotype of a binary relation with respect to its endotopisms is introduced and the endotype of an arbitrary equivalence relation is calculated.
Bibliography: 26 titles.

Keywords: endotopism, equivalence relation, regularity, coregularity, endotype.

UDC: 512.53

MSC: 20M20

Received: 13.01.2014

DOI: 10.4213/sm8325

 English version: Sbornik: Mathematics, 2014, 205:5, 646–662

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