On semimodular Mal'cev algebras
type: Item
instance of: scholarly article
title: On semimodular Mal'cev algebras
zbMATH Open document ID: 0627.17012
DOI: 10.1007/BF01190227
author: Alberto Elduque
published in: Archiv der Mathematik
publication date: 1988-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 17D10
zbMATH DE Number: 4019292
zbMATH Keywords: lower semimodular lattice of subalgebras
zbMATH Keywords: upper semimodular
zbMATH Keywords: non-split central simple non-Lie Mal'cev algebras
zbMATH Keywords: chain conditions
zbMATH Keywords: supersolvable
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4019292