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.

中文翻译：

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舒尔乘子和（残差）幂零李环

摘要 本文研究了 Schur 乘子的一些性质和李环的残差幂零性。在幂零李环的情况下，给定环之间特殊的同态，会得到一些同构。此外，我们将证明李环 L 的残余幂零与 L 的自由表示的选择无关。最后，我们给出了构造不属于特殊类的残余幂零李环的方法。