Frattini embeddings of ideals in modular Lie algebras
type: Item
instance of: scholarly article
title: Frattini embeddings of ideals in modular Lie algebras
zbMATH Open document ID: 0551.17003
DOI: 10.1007/BF01193908
author: David A. Towers
published in: Archiv der Mathematik
publication date: 1984-01-01T00:00:00Z
review text: In contrast to the characteristic zero the following result is proved: Every finite-dimensional Lie algebra over a field of characteristic \(p>0\) can be embedded in a Lie algebra with zero Frattini ideal. - More general, if B is an ideal of a Lie algebra L of characteristic \(p>0\) then there is a finite-dimensional Lie algebra M such that B is an ideal of M and \(B\cap \phi (L)=\phi (M)\) where \(\phi(X)\) is the Frattini ideal of X.
Mathematics Subject Classification ID: 17B50
Mathematics Subject Classification ID: 17B05
zbMATH DE Number: 3877380
zbMATH Keywords: embeddings in Lie algebras
zbMATH Keywords: prime characteristic
zbMATH Keywords: Frattini ideal
MaRDI profile type: Publication
cites work: Q5583129
cites work: A Frattini Theory for Algebras
cites work: On Complemented Lie Algebras
cites work: Frattini Embeddings of Normal Subgroups
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description: scientific article; zbMATH DE number 3877380