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.