Artinian rings with nilpotent adjoint group

• Datum: 2006
• Hauptverfasser: Evstaf’ev, R. Yu., Євстафьєв, Р. Ю.
• Format: Artikel
• Sprache: Ukrainisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2006
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/3464
• Назва журналу: 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 ^{...