Lie rings and the Engel condition (Q1239269)

In his work dealing with the restricted Burnside problem, Kostrikin showed that a Lie ring of prime characteristic \(p\) satisfying an \(n\)-th Engel condition, where \(n\leq p\), is locally nilpotent. Theorem 1 in the paper under review is an extension of this result to the case \(n= p+ 1, p\geq 3\). In proving Theorem 1, the author first proves Theorem 2: A Lie ring of characteristic \(p\geq 3\), without center, satisfying the \(p+ 1\) Engel condition and not satisfying the \(n\)-th Engel condition for \(n\leq p\), contains a non-trivial nilpotent ideal.