Ievstafiev R. Adjoint groups, construction and Lie structure of artinian rings

Artinian rings whose adjoint group or associated Lie ring is nilpotent, Engel, metabelian and supersolvable are considered. The structural theorem for artinian rings with nilpotent adjoint group is obtained. It is established that if the adjoint group of an artinian ring is weakly nilpotent or n-Engel then it is nilpotent. The construction of artinian rings whose adjoint group have a nilpotent commutator subgroup is described. It is proved that an artinian ring with the supersolvable adjoint group must be Lie supersolvable. An example of a Lie supersolvable ring with the non-supersolvable adjoint group is constructed.