Identities of Lie algebras with nilpotent commutator ideal over a field of finite characteristic (Q1311094)

All algebras considered are over a field \(K\) with char \(K=p \neq 0\). There exist examples of Lie algebras having no finite bases of identities [see \textit{V. Drenski}, Algebra Logika 13, 265-290 (1974; Zbl 0298.17011)]. The commutator ideals of these examples turned out to be \(p\)-nilpotent. The author of the note under review has shown that if the commutator ideal of a Lie algebra is \((p-1)\)-nilpotent then this Lie algebra has a finite basis of identities. Note that this implies that each Lie algebra of triangular matrices \(n \times n\), \(n \leq p\), has a finite basis of identities.