1. Let F be a field of prime characteristic different from 2 or 3 and L a Lie algebra over F with an abelian Cartan subalgebra H. For a in H* (the dual space of H) set La= {xCLI [xh] =ca(h)x, for all h in H}, and as usual, if La z(0), a is called a root with respect to H and La the root space for a. We have L0 = H and [LaLg] CLa+#. Seligman and Mills in [1 ] have called L a Lie algebra of classical type if L contains an abelian Cartan subalgebra H and if H and L satisfy: (i) [LL ] =L. (ii) L has center (0). (iii) L is a direct sum of subspaces La. (iv) If a is a nonzero root, then [LaLa] is one-dimensional. (v) If a is a nonzero root and J3CH*, then there is a positive integer m such that 1+ma is not a root. Let L be a Lie algebra over F such that LK is of classical type, where K is the algebraic closure of F. An extension field P of F is called a splitting field for L provided Lp is of classical type. We can now state the main theorem of this paper as: