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Exponentiation of relational systems with respect to strong homomorphisms. (English) Zbl 0929.08001

Summary: For any pair of \(n\)-ary relational systems \(G\), \(H\) we consider a certain power, i.e., an \(n\)-ary relational system carried by the set of all homomorphisms of \(H\) into \(G\). The subsystem of the power carried by the set of all strong homomorphisms of \(H\) into \(G\) is then taken as the power of \(G\) and \(H\) with respect to strong homomorphisms. The obtained binary operation of exponentiation of \(n\)-ary relational systems with respect to strong homomorphisms is studied and the results are applied to partial algebras.

MSC:

08A02 Relational systems, laws of composition
08A55 Partial algebras
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