On connection between reducibility of an n-ary quasigroup and that of its retracts

Abstract

An n-ary operation Q : Σn → Σ is called an n-ary quasigroup of order |Σ | if in the equation x0 = Q (x1, . . . , xn) knowledge of any n elements of x0, . . . , xn uniquely specifies the remaining one. An n-ary quasigroup Q is (permutably) reducible if Q (x1, . . . , xn) = P(R(xσ(1), . . . , xσ(k)), xσ(k+1), . . . , xσ(n)) where P and R are (n − k + 1)-ary… (More)
DOI: 10.1016/j.disc.2010.09.023

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