A Family of Closed Classes in k-Valued Logic

We consider functions of k-valued logic closed with respect to superposition classes containing all functions linear modulo k (these classes are related to divisors d of number k). Canonical relations are determined for the elements in such classes, and complete systems and bases are found. The lattice of the introduced classes with respect to the inclusion relation is described. Earlier results are generalized and complemented. This is true in particular for results on d-periodic functions and preservation of d-differences.