This article is cited in 5 papers

Correspondences of the Semigroup of Endomorphisms 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 terms of different constructions of the wreath product of a transformation semigroup with a small category and of the direct product of wreath products of groups, faithful representations of three correspondences of the semigroup of all endomorphisms of an arbitrary equivalence relation are described, namely, of the semigroup of all endotopisms, of the monoid of all strong endotopisms, and, correspondingly, of the group of all autotopisms of a given equivalence relation.

Keywords: wreath product, correspondence, endomorphism of an equivalence relation, endotopism, autotopism.

UDC: 512.53

Received: 21.03.2013
Revised: 19.06.2014

DOI: 10.4213/mzm10374

 English version: Mathematical Notes, 2015, 97:2, 201–212

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