Finite algebras with no independent basis of identities
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.
scientific article; zbMATH DE number 1226215