Document Type : Original Manuscript

Author

Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran.

Abstract

Let $L$ be a finite dimensional Lie algebra. A subalgebra $H$ of $L$ is called a $c^{\#}$-ideal of $L$, if there is an ideal $K$ of $L$ with $L=H+K$ and $H\cap K$ is a $CAP$-subalgebra of $L$. This is analogous to the concept of a $c^{\#}$-normal subgroup of a finite group. Now, we consider the influence of this concept on the structure of finite dimentional Lie algebras.

Keywords

###### ##### References
1. D. W. Barnes, On the cohomology of soluble Lie algebras, Math. Z., 101 (1967), 343–349.

2. A. R. Salemkar, S. Chehrazi and F. Tayanloo, Characterizations for supersolvableLie algebras, Comm. Algebra, 41 (2013), 2310–2316.

3. D. A. Towers, A Frattini theory for algebras, Proc. London Math. Soc., 27 (1973), 440–462.

4. D. A. Towers, C-ideals of Lie algebras, Comm. Algebra, 37 (2009), 4366–4373.
5. D. A. Towers, Subalgebras that cover or avoid chief factors of Lie algebras, Proc. Amer. Math. Soc., 143 (2015), 3377–3385.

6. Y. Wang and H. Wei, c#-Normality of groups and its properties, Algebr Represent Theor, 16 (2013), 193–204.

7. Y. Wang, C-normality of groups and its properties, J. Algebra, 180 (1996), 954–965.