Geodesic
Stable binary relations on universal algebras
Sbornik. Mathematics, Tome 11 (1970) no. 2, pp. 145-155

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With every universal algebra there is associated the ordered involutory semigroup of all its correspondences (stable binary relations). Two universal algebras are said to be $R$-isomorphic if their semigroups of correspondences are isomorphic. A subclass $K$ of the class $C$ of universal algebras is $R$-characterizable in $C$ if it is closed with respect to $R$-isomorphisms. In this article we single out a number of $R$-characterizable classes of universal algebras. It is shown that the complete preimage of an $R$-characterizable class is $R$-characterizable. The results obtained are applied to classes of semigroups and semiheaps. Bibliography: 6 titles. 
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     author = {G. I. Zhitomirskii},
     title = {Stable binary relations on universal algebras},
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G. I. Zhitomirskii. Stable binary relations on universal algebras. Sbornik. Mathematics, Tome 11 (1970) no. 2, pp. 145-155. http://geodesic.mathdoc.fr/item/SM_1970_11_2_a0/