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Lie ring

From Encyclopedia of Mathematics
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A ring that satisfies the conditions

and

(the Jacobi identity), where are any elements of . The first of these conditions implies that 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: http://encyclopediaofmath.org/index.php?title=Lie_ring&oldid=32508
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article