C-Ideals of Lie Algebras.

Towers, David A. (2009) C-Ideals of Lie Algebras. Communications in Algebra, 37 (12). pp. 4366-4373. ISSN 0092-7872

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A subalgebra B of a Lie algebra L is called a c-ideal of L if there is an ideal C of L such that L = B + C and B \cap C \leq B_L, where B_L is the largest ideal of L contained in B. This is analogous to the concept of c-normal subgroup, which has been studied by a number of authors. We obtain some properties of c-ideals and use them to give some characterisations of solvable and supersolvable Lie algebras. We also classify those Lie algebras in which every one-dimensional subalgebra is a c-ideal.

Item Type:
Journal Article
Journal or Publication Title:
Communications in Algebra
Additional Information:
The final, definitive version of this article has been published in the Journal, Communications in Algebra, 37 (12), 2009, © Informa Plc
Uncontrolled Keywords:
?? lie algebrasc-idealnilpotentsolvablesupersolvablefrattini ideal.algebra and number theoryqa mathematics ??
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Deposited On:
18 Nov 2008 09:55
Last Modified:
15 Jul 2024 09:47