A morphic ring of neat range one

• Date: 2016
• Main Authors: Pihura, Oksana, Zabavsky, Bohdan
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2016
• Subjects: Bezout ring; neat ring; clear ring; elementary divisor ring; stable range one; neat range one; 13F99
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/57
• Journal Title: Algebra and Discrete Mathematics

We show that a commutative ring \(R\) has neat range one if and only if every unit modulo principal ideal of a ring lifts to a neat element. We also show that a commutative morphic ring \(R\) has a neat range one if and only if for any elements \(a, b \in R\) such that \(aR=bR\) there exist neat ele...