A decomposition theorem for semiprime rings

• Date: 2018
• Main Author: Khibina, Marina
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: minor of a ring; local idempotent; semiprime ring; Peirce decomposition; 16P40; 16G10
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/916
• Journal Title: Algebra and Discrete Mathematics

A ring \(A\) is called an \(FDI\)-ring if there exists a decomposition of the identity of \(A\) in a sum of finite number of pairwise orthogonal primitive idempotents. We call a primitive idempotent \(e\) artinian if the ring \(eAe\) is Artinian. We prove that every semiprime \(FDI\)-ring is a direc...