Artinian rings with nilpotent adjoint group

  • R. Yu. Evstaf’ev


Let $R$ be an Artinian ring (not necessarily with unit element), let $Z(R)$ be its center, and let $R ^{\circ}$ 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 $R ^{\circ}$ is nilpotent and the set $Z (R) + R ^{\circ}$ 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.
How to Cite
Evstaf’ev, R. Y. “Artinian Rings With Nilpotent Adjoint Group”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, no. 3, Mar. 2006, pp. 417–426,
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