On Leibniz algebras with maximal cyclic subalgebras
We begin to study the structure of Leibniz algebras having maximal cyclic subalgebras.
On some properties of the upper central series in Leibniz algebras
This article discusses the Leibniz algebras whose upper hypercenter has finite codimension. It is proved that such an algebra includes a finite dimensional ideal such that the factor-algebra is hypercentral. This result is an extension to the Leibniz algebra of the corresponding result obtained earlier for Lie algebras. It is also analogous to the corresponding results obtained for groups and modules.
On the rings on torsion-free groups
On the subgroups of completely decomposable torsion-free groups that are ideals in every ring
In this paper we consider completely decomposable torsion-free groups and we determine the subgroups which are ideals in every ring over such groups.