Rings with finite decomposition of identity

• Date: 2011
• Main Authors: Dokuchaev, M. A., Gubareni, N. M., Kirichenko, V. V., Докучаєв, М. А., Губарені, Н. М., Кириченко, В. В.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2011
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2719
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

A criterion for semiprime rings with finite decomposition of identity to be prime is given. We also give a short survey on some finiteness conditions related to the decomposition of identity. We consider the notion of a net of a ring and show that the lattice of all two-sided ideals of a right sem...