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

## 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: | ?? qa ?? |

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: | 26 May 2017 01:20 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/19877 |
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