On a power of $n$-ary relational systems carried by strong homomorphisms

摘要

In this paper, we introduce and study a new operation of product of n-ary relational systems which lies between their direct product andthe direct product of their reflexive hulls. Moreover, we study the subsystem of the direct power of n-ary relatioal systems carried bythe strong homomorphisms. We show that, with respect to the product introduced and the strong homomorphisms, weak forms of the first andsecond exponential laws are valid and the third exponential law is satisfied.