Geodesic
Stable binary relations on universal algebras
Sbornik. Mathematics, Tome 11 (1970) no. 2, pp. 145-155 
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/
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     author = {G. I. Zhitomirskii},
     title = {Stable binary relations on universal algebras},
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     volume = {11},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1970_11_2_a0/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] A. G. Kurosh, Lektsii po obschei algebre, Fizmatgiz, Moskva, 1962 | MR

[2] E. S. Lyapin, Polugruppy, Fizmatgiz, Moskva, 1960 | MR

[3] V. V. Vagner, Teoriya otnoshenii i algebra chastichnykh otobrazhenii, Teoriya polugrupp i ee prilozheniya, Saratov, 1965 | MR

[4] Zh. Rige, “Binarnye otnosheniya, zamykaniya, sootvetstviya Galua”, Kibern. sb., 7 (1963), 129–185

[5] V. V. Vagner, “Teoriya obobschennykh grud i obobschennykh grupp”, Matem. sb., 32(74) (1953), 545–632 | MR | Zbl

[6] N. Burbaki, Teoriya mnozhestv, Mir, Moskva, 1965