Lie ring

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A ring $A$ that satisfies the conditions




(the Jacobi identity), where $a,b,c$ are any elements of $A$. The first of these conditions implies that $A$ is anti-commutative:


The Lie rings form a variety of rings, in general non-associative. It contains, however, all rings with zero multiplication.

See also Non-associative rings and algebras.

How to Cite This Entry:
Lie ring. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article