Artinian rings with nilpotent adjoint group - Evstaf’ev, R. Yu. (Ukrains’kyi Matematychnyi Zhurnal, 2006)
Let R be an Artinian ring (not necessarily with unit element), let Z(R) be its center, and let R ^° be the group of invertible elements of the ring R with respect to the operation a ∘ b = a + b + ab. We prove that the adjoint group R ^° is nilpotent and the set Z (R) + R ^° generates R as a ring if and only if R is the direct sum of finitely many ideals each of which is either a nilpotent ring or a local ring with nilpotent multiplicative group.