Plane modules and distributive rings

• Date: 1993
• Main Authors: Tuganbaev, A. A., Туганбаев, А. А.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 1993
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5860
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

Let $A$ be a semiprime ring entire over its center. We prove that the following conditions are equivalent: (a) A is a ring distributive from the right (left); (b) w.gl. $\dim (A) ≤ 1$; moreover, if $M$ is an arbitrary prime ideal of the ring $A$, then $A/M$ is a right Ore set.