The Core of Inner ideal of Real Four Dimensional Lie Algebra With One Dimensional Derived

Suppose that V is any inner ideal of L. The core of V is an inner ideal of L with special requirement. In this paper we prove. If L is a 4-dimension Lie algebra a with 1-dimensional derived , then the core of every inner ideal of L is zero. Moreover L containing a sandwich elements if L' not subset of Z and every element in L is sandwich if L' subset of Z. .