Polynomial k-ary operations, matrices, and k-mappings

G. BELYAVSKAYA

Abstract

We establish connection between product of two matrices of order k  k over a eld and the product of the k-mappings corresponding to the k-operations, dened by these matrices. It is proved that, in contrast to the binary case, for arity k  3 the components of the k-permutation inverse to a k-permutation, all components of which are polynomial k-quasigroups, are not necessarily k-quasigroups although are invertible at least in two places. Some transformations with the help of permutations of orthogonal systems of polynomial k-operations over a eld are considered.