Simple Lie ring

Definition
A Lie ring is said to be simple if it has no proper nonzero ideals. A related notion is that of simple Lie algebra. Note that while any simple Lie ring which is also a Lie algebra over a field must be a simple Lie algebra, there could be simple Lie algebras which are not simple as Lie rings. For instance, any one-dimensional Lie algebra over a field is simple as a Lie algebra, but not as a Lie ring.