Geodesic
Solvable just-non-Cross varieties of Lie rings
Sbornik. Mathematics, Tome 29 (1976) no. 3, pp. 345-358

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A variety of Lie rings is called just-non-Cross if it itself is not Cross, but each of its proper subvarieties is Cross, i.e. is generated by a finite ring. In this paper, we completely describe the solvable just-non-Cross varieties both of Lie rings and of Lie $R$-algebras where $R$ is a finite commutative ring with identity and, in particular, where $R$ is a finite field. We find algorithms which allow us to determine whether a given identity defines a Cross variety of Lie algebras; also, using the multiplication and addition tables of a finite Lie algebra, we find algorithms for extracting its identities. Bibliography: 10 titles. 
@article{SM_1976_29_3_a3,
     author = {Yu. A. Bahturin and A. Yu. Ol'shanskii},
     title = {Solvable {just-non-Cross} varieties of {Lie} rings},
     journal = {Sbornik. Mathematics},
     pages = {345--358},
     publisher = {mathdoc},
     volume = {29},
     number = {3},
     year = {1976},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1976_29_3_a3/}
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Yu. A. Bahturin; A. Yu. Ol'shanskii. Solvable just-non-Cross varieties of Lie rings. Sbornik. Mathematics, Tome 29 (1976) no. 3, pp. 345-358. http://geodesic.mathdoc.fr/item/SM_1976_29_3_a3/