Open Access
2010 Polynomial $k$-ary operations, matrices, and $k$-mappings
J. Gen. Lie Theory Appl. 4: 1-8 (2010). DOI: 10.4303/jglta/G100301


We establish connection between product of two matrices of order $k\times k$ 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 $k\geq 3$ 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.


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G. BELYAVSKAYA. "Polynomial $k$-ary operations, matrices, and $k$-mappings." J. Gen. Lie Theory Appl. 4 1 - 8, 2010.


Published: 2010
First available in Project Euclid: 11 October 2011

zbMATH: 1213.20068
MathSciNet: MR2795571
Digital Object Identifier: 10.4303/jglta/G100301

Primary: 05B15 , 20N05 , 20N15

Rights: Copyright © 2010 Ashdin Publishing (2009-2013) / OMICS International (2014-2016)

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