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On \(B\)-algebras and quasigroups. (English) Zbl 0994.08003

A groupoid \((Q,\cdot)\) is a \(B\)-algebra if for all \(x,y,z\in Q\) there hold \(xx=0\), \(x0=x\), \((xy)z = x(z(0y))\), where \(0\) is some fixed element of \(Q\). It is proved that such an algebra is a quasigroup.

MSC:

08A62 Finitary algebras
20N05 Loops, quasigroups
06F35 BCK-algebras, BCI-algebras
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