Bilun S. Associative algebras and Lie algebras with some restrictions on the systems of subalgebras and ideals

The dissertation is devoted to the investigation of the structure of sums of Lie algebras and sums of associativealgebras. In the the first chapter we make a short review of the literature connected with the topics studied in the dissertation.In the second chapter we collect basic definitions and important facts that are uses in the subsequent chapters. The thirdchapter is devoted to finite dimensional Lie algebras over algebraically closed fields of characteristic zero, which can bedecomposed into a sum of an abelian subalgebra and a subalgebra with nonzero center. We prove that in such an algebra thecenter of the subalgebra lies in the radical of the algebra .The fourth chapter deals with fite dimensional Lie algebras endowedwith abelian complex structures.