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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 charF ≠ 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 Mn(A) are also presented.