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Belousov equations on quasigroups. (English) Zbl 0645.39006
A balanced equation \(w_ 1=w_ 2\) is one in which each variable appears precisely once on both sides. The set of variables in the term \(u\) is denoted by \(<u>\). A balanced equation is called Belousov if for every subterm \(u_ i\) of \(w_ i\) there exists a subterm \(v_ j\) of \(w_ j\) \((i,j=1,2)\) such that \(<u_ i>=<v_ j>\). V. D. Belousov [Math. Sb. (N.S.) 70(112), 55-97 (1966; Zbl 0199.05203)] showed that every Belousov equation is equivalent to a finite set of inseparable Belousov equations. In this paper the authors prove that any finite set of Belousov equations is equivalent to a single inseparable Belousov equation with no isolated variables.
Reviewer: M.Csikós

39B52 Functional equations for functions with more general domains and/or ranges
20N05 Loops, quasigroups
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