Abstract
In this article, some properties of the Schur multiplier and residual nilpotency of Lie rings are studied. In the case of nilpotent Lie rings and given special homomorphism between rings, some isomorphisms will be obtained. Furthermore, we will prove that the residual nilpotent of a Lie ring L is independent of the choice of the free presentation of L. Finally, we give a method of constructing residually nilpotent Lie rings which do not belong to the special class.
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