Subalgebras of finitely defined Lie algebras (Q1145203)

In 1972 the reviewer [Izv. Akad. Nauk SSSR, Ser. Mat. 36, 1173--1219 (1972; Zbl 0252.02046)] posed the following question: Is any recursively presented (r.p.) Lie algebra over a simple field embeddable in a finitely presented (f.p.) Lie algebra? The paper gives the positive answer to this question. So, the variety of Lie algebras over a simple field (and also the variety of Lie rings) is a Higman variety (a variety \(\mathfrak M\) of universal algebras is called Higman variety if every r. p. algebra from \(\mathfrak M\) is embeddable in a f.p. algebra from \(\mathfrak M\)).