Finite algebras with no independent basis of identities (Q1272124)

For a finite field \(\Phi \), let \(\mathcal P\) be the variety of linear \(\Phi \)-algebras satisfying the identity \(x(yz)=0\). It was proved by \textit{S. V. Polin} [Sib. Mat. Zh. 17, No. 6, 1356-1366 (1976; Zbl 0353.17003)] that \(\mathcal P\) contains finite algebras without finite bases of identities. The author shows that there exist also finite algebras of \(\mathcal P\) with no independent basis for its identities.