Abstract
We consider a Lie algebraL over an arbitrary field that is decomposable into the sumL=A+B of an almost Abelian subalgebraA and a subalgebraB 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.
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