Primitive elements of free LIE algebras

Let A be a free algebra generated by a finite set X . Firstly, by using partialderivations of an element a of A some basic results have been obtained.Afterwards, by giving definition of admissible sets some theorems with respect tothese sets have been proved. The rank of an element a of A is defined as theminumum number of elements of X appearing in images of a under automorphismsof A . It has been proved that the rank of an element a of A is equal to the rank offree module generated by partial derivations of a . If a system of elements of A issubset of a free generators of A , it is called a primitive system. Later it has beenproved that an endomorphism of A mapping primitive elements of A onto primitiveelements is an automorphism.Key Words: Free algebras, partial derivations, admissible sets.II