On Rings with Weakly Prime Centers

• Date: 2014
• Main Authors: Wei, Junchao, Вей, Юнчао
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2014
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2250
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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...