On the overstructure of a class of polynomials in many-valued logics

For the functional system $P_k$, where $k=p^r$, $p$ is a prime number and $r\ge 2$, we give a representation by formulae of functions of the class $\frak M_k$ which consists of the functions preserving congruence modulo $d=p^s$, $s=1,\ldots,r-1$. Basing on this representation, we describe several closed classes, which include the class of polynomials $\Pol_k$ and are contained in the class $\frak M_k$, and give some properties of the classes introduced.
This work is supported by the Russian Foundation for Basic Research, Grant 94–01–01206–a.