Lie ring
From HandWiki
A ring $A$ that satisfies the conditions
$$a^2=0$$
and
$$(ab)c+(bc)a+(ca)b=0$$
(the Jacobi identity), where $a,b,c$ are any elements of $A$. The first of these conditions implies that $A$ is anti-commutative:
$$ba=-ab.$$
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.
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