Lie ring
From Encyclopedia of Mathematics
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=15526
Lie ring. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Lie_ring&oldid=15526
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article