Polynomial k - ary operations , matrices , and k - mappings
نویسنده
چکیده
We establish connection between product of two matrices of order k × k over a field and the product of the k-mappings corresponding to the k-operations, defined 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 field are considered. 2000 MSC: 20N05, 20N15, 05B15
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