Frattini embeddings of ideals in modular Lie algebras (Q801148)

In contrast to the characteristic zero the following result is proved: Every finite-dimensional Lie algebra over a field of characteristic \(p>0\) can be embedded in a Lie algebra with zero Frattini ideal. - More general, if B is an ideal of a Lie algebra L of characteristic \(p>0\) then there is a finite-dimensional Lie algebra M such that B is an ideal of M and \(B\cap \phi (L)=\phi (M)\) where \(\phi(X)\) is the Frattini ideal of X.