Abstract
We describe one-sided identity elements and subsets of the semigroup of all binary relations on a nonempty set. We obtain formulas for the number of identities for a finite set.
Similar content being viewed by others
Literature cited
K. A. Zaretskii, “The semigroup of binary relations,” Mat. Sb.,61, No. 3, 291–305 (1963).
A. Clifford and G. Preston, The Algebraic Theory of Semi-groups [Russian translation], Vol. 1, Mir, Moscow (1972).
K. Kuratowski and A. Mostowskii, The Theory of Sets [Russian translation], Mir, Moscow (1970).
E. S. Lyapin, Semigroups [in Russian], Fizmatgiz, Moscow (1960).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 8, pp. 1026–1031, August, 1990.
Rights and permissions
About this article
Cite this article
Diasamidze, Y.I. One-sided identities for subsets of the semigroup of binary relations. Ukr Math J 42, 915–918 (1990). https://doi.org/10.1007/BF01099220
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01099220