Rigid, quasi-rigid and matrix rings with \((\overline{\sigma},0)\)multiplication

• Date: 2018
• Main Authors: Abdioglu, Cihat, Şahinkaya, Serap, KÖR, Arda
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: simple \(0\)-multiplication; quasi \(\sigma\)-rigid rings; 16N60,16S36,16W60
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1020
• Journal Title: Algebra and Discrete Mathematics

Let \(R\) be a ring with an endomorphism \(\sigma\). We introduce \((\overline{\sigma}, 0)\)-multiplication which is a generalization of the simple \( 0\)- multiplication. It is proved that for arbitrary positive integers \(m\leq n\) and \(n\geq 2\), \(R[x; \sigma]\) is a reduced ring if and only if...