GENERALIZED LIE NILPOTENT GROUP RINGS

Abstract

Let be the group ring of a group over a ring with identity. The ring is said to be Lie -nilpotent if for every sequence of elements of there is an index such that the Lie commutator . It is proved that is a Lie -nilpotent ring if and only if is Lie -nilpotent and one of the following conditions is satisfied: 1) is an Abelian group, or 2) is a ring of characteristic ( prime), is a nilpotent group and its commutator subgroup is a finite -group.Bibliography: 3 titles.