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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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