On semimodular Mal'cev algebras
Malcev algebras with an upper or lower semimodular lattice of subalgebras are studied in this paper. For the upper semimodular case, the non-split central simple non-Lie Malcev algebras turn out to be the only examples which are not Lie algebras. The known results for Lie algebras with a lower semimodular lattice of subalgebras [see, for instance, \textit{A. G. Gejn} [Sib. Mat. Zh. 17, 243-248 (1976; Zbl 0342.17010)] and \textit{A. G. Gejn} and \textit{Yu. N. Mukhin} [Mat. Zap. 12, No.2, 24-48 (1980; Zbl 0479.17008)] are extended for Malcev algebras.
lower semimodular lattice of subalgebras
non-split central simple non-Lie Mal'cev algebras
scientific article; zbMATH DE number 4019292
scientific article