On Artinian rings satisfying the Engel condition

• Date: 2006
• Main Authors: Evstaf’ev, R. Yu., Евстафьев, Р. Ю.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2006
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3527
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

Let $R$ be an Artinian ring, not necessarily with a unit element, and let $R^{\circ}$ be the group of all invertible elements of $R$ under the operation $a \circ b = a + b + ab.$ We prove that $R^{\circ}$ is a nilpotent group if and only if it is an Engel group and the ring $R$ modulo its Jacobson...