Geodesic
The endotopism semigroups of an equivalence relation
Sbornik. Mathematics, Tome 205 (2014) no. 5, pp. 646-662

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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: regularity, coregularity, endotype.
Mots-clés : endotopism, equivalence relation 
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Yu. V. Zhuchok; E. A. Toichkina. The endotopism semigroups of an equivalence relation. Sbornik. Mathematics, Tome 205 (2014) no. 5, pp. 646-662. http://geodesic.mathdoc.fr/item/SM_2014_205_5_a2/