  In this work, we extend the definition of the graded prime ideals from those
in commutative graded rings to the ideals over graded Lie algebras. We prove
some facts about graded prime Lie ideals in arbitrary Lie algebras that are
similar to those about graded prime ideals over a commutative or
non-commutative ring.In addition, the ideas of graded semiprime Lie ideals and
graded total prime Lie ideals will be introduced.
