Artinian rings with nilpotent adjoint group

  • R. Yu. Evstaf’ev

Abstract

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.
Published
25.03.2006
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, https://umj.imath.kiev.ua/index.php/umj/article/view/3464.
Section
Short communications