Modularity in Malcev algebras
type: Item
instance of: scholarly article
title: Modularity in Malcev algebras
zbMATH Open document ID: 0543.17013
DOI: 10.1007/BF01237857
published in: Archiv der Mathematik
publication date: 1985-01-01T00:00:00Z
review text: If \(H\) is a subalgebra of a Malcev algebra \(M\) we define \(H_M\), the core of \(H\) in \(M\), as the largest ideal of \(M\) contained in \(H\). We say that \(H\) is core-free in \(M\) if \(H_M=0\). In this paper we study analogous concepts to those of quasi-ideal and modular subalgebra in Lie algebras for Malcev algebras in order to make use of them to study the structure of Malcev algebras which have a nontrivial core-free modular subalgebra. We state the main results of this paper: (i) If \(Q\) is a quasi-ideal of a Malcev algebra \(M\) (finite or infinite dimensional over a field of characteristic not two such that \(Q\) is not an ideal of \(M\), then \(M/Q_M\) is a Lie algebra. - (ii) If \(H\) is a modular subalgebra of a finite-dimensional Malcev algebra \(M\) over a field of characteristic zero such that \(H\) is not an ideal of \(M\), then \(M/H_M\) is a Lie algebra.
Mathematics Subject Classification ID: 17D10
Mathematics Subject Classification ID: 17B30
Mathematics Subject Classification ID: 17B05
zbMATH DE Number: 3863431
zbMATH Keywords: Fitting decomposition
zbMATH Keywords: Frattini subalgebra
zbMATH Keywords: Lie algebra structure
zbMATH Keywords: core-free modular subalgebra
zbMATH Keywords: quasi-ideal
zbMATH Keywords: infinite dimensional
zbMATH Keywords: characteristic not two
zbMATH Keywords: finite-dimensional Malcev algebra
zbMATH Keywords: characteristic zero
author: Alfy Abd El Malek
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3863431