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Canonical decomposition of \(n\)-ary quasigroups. (Russian) Zbl 0648.20069
An n-quasigroup (Q,A) is decomposable if there exists \(\sigma \in S_ n\), \(1<k<n\), a k-quasigroup (Q,B) and an \((n-k+1)\)-quasigroup (Q,C) such that \[ A(x^ n_ 1)=B(C(x_{\sigma (1)},...,x_{\sigma (k)}),x_{\sigma (k+1)},...,x_{\sigma (n)}). \] It is proved that the so-called canonical decomposition of an n-ary quasigroup into a binary loop and k-ary quasigroups is unique with respect to principal isotrophies of components of the same arity.
Reviewer: W.A.Dudek

MSC:
20N15 \(n\)-ary systems \((n\ge 3)\)
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