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## Abstract

A Lie ideal of a division ring

*A*is an additive subgroup*L*of*A*such that the Lie product [*l*,*a*] =*la*−*al*of any two elements*l*∈*L*,*a*∈*A*is in*L*or [*l*,*a*] ∈*L*. The main concern of this paper is to present some properties of Lie ideals of*A*which may be interpreted as being dual to known properties of normal subgroups of*A*∗. In particular, we prove that if*A*is a finite-dimensional division algebra with center*F*and char*F*≠ 2, then any finitely generated Z-module Lie ideal of*A*is central. We also show that the additive commutator subgroup [*A*,*A*] of*A*is not a finitely generated Z-module. Some other results about maximal additive subgroups of*A*and*M*_{n}(*A*) are also presented.Original language | English |
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Article number | 1850049 |

Number of pages | 6 |

Journal | Journal of algebra and its applications |

Volume | 17 |

Issue number | 03 |

Early online date | 7 Apr 2017 |

DOIs | |

Publication status | Published - Mar 2018 |

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