On Rings with Weakly Prime Centers

  • Junchao Wei

Abstract

We introduce a class of rings obtained as a generalization of rings with prime centers. A ring $R$ is called weakly prime center (or simply $WPC$) if $ab \in Z(R)$ ($R$) implies that $aRb$ is an ideal of $R$ where $Z(R)$ stands for the center of $R$. The structure and properties of these rings are studied and the relationships between prime center rings, strongly regular rings, and WPC rings are discussed, parallel with the relationship between the $WPC$ and commutativity.
Published
25.12.2014
How to Cite
WeiJ. “On Rings With Weakly Prime Centers”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, no. 12, Dec. 2014, pp. 1615–1622, http://umj.imath.kiev.ua/index.php/umj/article/view/2250.
Section
Research articles