# On the sum of an almost abelian Lie algebra and a Lie algebra finite-dimensional over its center

### Abstract

We consider a Lie algebra*L*over an arbitrary field that is decomposable into the sum

*L=A+B*of an almost Abelian subalgebra

*A*and a subalgebra

*B*finite-dimensional over its center. We prove that this algebra is almost solvable, i.e., it contains a solvable ideal of finite codimension. In particular, the sum of the Abelian and almost Abelian Lie algebras is an almost solvable Lie algebra.

Published

25.05.1999

How to Cite

*Ukrains’kyi Matematychnyi Zhurnal*, Vol. 51, no. 5, May 1999, pp. 636–644, https://umj.imath.kiev.ua/index.php/umj/article/view/4650.

Issue

Section

Research articles