Finite-dimensional right alternative algebras that do not generate finitely based varieties (Q1089088)

The class of right-alternative algebras is defined by the following two identities: \((xy)y=xy^ 2,\quad ((xy)z)y=x((yz)y).\) It is known [\textit{I. V. L'vov}, Algebra Logika 17, No.3, 282-286 (1978; Zbl 0414.17009)] that any finite alternative algebra has a finite basis of identities. An example of a finite dimensional right-alternative algebra over an arbitrary field which has not any finite basis of identities is constructed. This one gives a negative answer to the corresponding question posed by \textit{I. V. L'vov} [in Dnestrovskaya tetrad', Novosibirsk (1982; Zbl 0493.16001)].