Artinian rings with nilpotent adjoint group

• Date: 2006
• Main Authors: Evstaf’ev, R. Yu., Євстафьєв, Р. Ю.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2006
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3464
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 ^{...