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Quasigroups with completely reducible balanced identities. (Russian) Zbl 0587.20037
An identity \(W_ 1=W_ 2\) is balanced if each variable appears exactly twice in the identity, once on each side. A balanced identity is reducible when the following conditions hold: If \(W_ 1\) contains a subword xy then \(W_ 2\) also contains xy or yx. If \(W_ 1=xu\) or \(W_ 1=ux\) then \(W_ 2=xv\) or \(W_ 2=vx\) (x and y are variables, u and v are subwords). Generalising this definition the author defines the quasigroups mentioned in the title. He proves that every completely reducible balanced identity falls into pieces of a system of such identities.
Reviewer: M.Csikós

MSC:
20N05 Loops, quasigroups
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