The Frattini Theory Of Restricted Lie Color Algebra

This paper mainly consider some basic theory of Frattini p-subalgebra of restricted Lie color algebra from four aspects. First,we give some basic concepts of restricted Lie color algebra,for example,p-subalgebra,p-idea and p-nilpotent Lie color algebra. Several elementary properties of restricted Lie color algebra are collated. They are the base of my following research work. We then obtain some elementary results of the Frattini subalgebra and the Frattini p-subalgebra of a restricted Lie color algebra, show that the fact that both the Frattini p-subalgebra and the Frattini subalgebra of a solvable restricted Lie color algebra are its two nilpotent ideals. Moreover,φ_p- free andφ—free restricted Lie color algebra are discussed and their several sufficient and neccessary condtions are found. On the other hand, we give the concepts of p-elementary and E-p-restricted Lie color algebra, and obtain a series of properties.