  Following the structure theory approach for rings, the aim of this paper is
to study some distinguished classes of Lie algebras. We introduce the notion of
a Lie-module and discuss some relations of it with various classes of ideals of
a Lie algebra. We give several Lie-module-related characterizations of
primitive Lie algebras and prove a representation theorem of a Lie algebra in
terms of primitive Lie algebras. We prove a density theorem. Finally, we
highlight on the importance of nuclear ideals of prime and semiprime Lie
algebras in determining them.
