On radical square zero rings

• Date: 2018
• Main Authors: Ringel, Claus Michael, Xiong, Bao-Lin
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: Artin algebras; left artinian rings; representations; modules; Gorenstein modules; CM modules; self-injective algebras; radical square zero algebras; 16D90; 16G10; 16G70
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/727
• Journal Title: Algebra and Discrete Mathematics

Let \(\Lambda\) be a connected left artinian ring with radical square zero and with \(n\) simple modules. If \(\Lambda\)  is not self-injective, then we show that any module \(M\) with \(\operatorname{Ext}^i(M,\Lambda) = 0\) for \(1 \le i \le n+1\) is projective. We also determine the structure of t...