Identities in almost nilpotent Lie rings

The following Lie rings $L$ are shown to have finite bases for their identities. (i) $L$ has a finite ideal $K$ with $L/K$ nilpotent. (ii) $L$ has a nilpotent ideal $N$ of finite index with $\operatorname{ad}x$ nilpotent on $N$ for each $x\in L$. (iii) $L$ is soluble, algebraic and possesses a nilpotent ideal of finite index. Of independent interest are some other results giving characterizations of certain classes of varieties of Lie rings.
Bibliography: 17 titles.