Binary Relations as Lattice Isomorphisms
نویسندگان
چکیده
In 1963, Zaretskiùõ established a one-to-one correspondence between the set BX of binary relations on a set X and the set of triples of the form (W,φ, V ) where W and V are certain lattices and φ : W −→ V is an isomorphism. We provide a multiplication for these triples making the Zaretskiùõ correspondence a semigroup isomorphism. In addition, we consider faithful representations of BX by pairs of partial transformations and also as the translational hull of its rectangular relations. Using these triples, we study idempotents, regular and completely regular elements and relations H-equivalent to some relations with familiar properties such as reßexivity, transitivity, etc.
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