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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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    Abstract

    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: 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 algebras ; c-ideal ; nilpotent ; solvable ; supersolvable ; Frattini ideal.
    Subjects: Q Science > QA Mathematics
    Departments: Faculty of Science and Technology > Mathematics and Statistics
    ID Code: 19877
    Deposited By: Dr David A. Towers
    Deposited On: 18 Nov 2008 09:55
    Refereed?: Yes
    Published?: Published
    Last Modified: 09 Oct 2013 12:43
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/19877

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