Residual finiteness and the Noetherian property of finitely generated Lie algebras

A description of locally Noetherian varieties of Lie algebras over a field of characteristic zero is obtained. Also described are the locally residually finite subvarieties of special, locally solvable, and some other varieties of Lie algebras over an infinite field of positive characteristic. Sufficient conditions for the residual finiteness and Noetherian property of finitely generated Lie algebras are found.
Bibliography: 13 titles.