Subring of a Lie ring
From Groupprops
Definition
Let be a Lie ring and
be a subset of
. We say that
is a subring of
, or a Lie subring, if it satisfies the following equivalent conditions:
-
is a subgroup of the additive group of
and is closed under the Lie bracket of
.
-
is a Lie ring with the addition and Lie bracket operations induced from
.