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One-sided identities for subsets of the semigroup of binary relations

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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.

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Literature cited

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    K. A. Zaretskii, “The semigroup of binary relations,” Mat. Sb.,61, No. 3, 291–305 (1963).

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    A. Clifford and G. Preston, The Algebraic Theory of Semi-groups [Russian translation], Vol. 1, Mir, Moscow (1972).

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    K. Kuratowski and A. Mostowskii, The Theory of Sets [Russian translation], Mir, Moscow (1970).

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    E. S. Lyapin, Semigroups [in Russian], Fizmatgiz, Moscow (1960).

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 8, pp. 1026–1031, August, 1990.

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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

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  • Binary Relation
  • Identity Element