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C-Ideals of Lie Algebras.

Research output: Contribution to journalJournal article

Published

Journal publication date12/2009
JournalCommunications in Algebra
Journal number12
Volume37
Number of pages8
Pages4366-4373
Original languageEnglish

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.

Bibliographic note

The final, definitive version of this article has been published in the Journal, Communications in Algebra, 37 (12), 2009, © Informa Plc