Effective ring

• Date: 2018
• Main Authors: Zabavsky, B. V., Kuznitska, B. M.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: Bezout ring; exchange ring; clean ring; effective ring; elementary divisor ring; idempotent of stable range 1; neat ring; 13F99
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1052
• Journal Title: Algebra and Discrete Mathematics

In this paper we will investigate commutative Bezout domains whose finite homomorphic images are semipotent rings. Among such commutative Bezout rings we consider a new class of rings and call them an effective rings. Furthermore we prove that effective rings are elementary divisor rings.