  We study Lie algebras generated by extremal elements (i.e., elements spanning
inner ideals of L) over a field of characteristic distinct from 2. We prove
that any Lie algebra generated by a finite number of extremal elements is
finite dimensional. The minimal number of extremal generators for the Lie
algebras of type An, Bn (n>2), Cn (n>1), Dn (n>3), En (n=6,7,8), F4 and G2 are
shown to be n+1, n+1, 2n, n, 5, 5, and 4 in the respective cases. These results
are related to group theoretic ones for the corresponding Chevalley groups.
