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Abstract
D. A. Towers introduced the notion of ideal index of a maximal subalgebra of a Lie algebra, and used it to analyze the influence of maximal subalgebras on the structure of a finite dimensional Lie algebras.
In this article, we generalize the ideal index from maximal subalgebras to all subalgebras, and obtain some new characterizations of solvable and supersolvable Lie algebras by the ideal indices of some certain subalgebras.
ACKNOWLEDGMENT
The authors would like to thank the referee for his/her valuable suggestions, which was made the improvement of the paper.
Notes
Communicated by A. Elduque.