A criterion of elementary divisor domain for distributive domains

• Date: 2017
• Main Authors: Bokhonko, Vasylyna, Zabavsky, Bohdan Volodymyrovych
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2017
• Subjects: Distributive domain; Bezout duo-domain; 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/58
• Journal Title: Algebra and Discrete Mathematics

In this paper we introduce the notion of the neat range one for Bezout duo-domains. We show that a distributive Bezout domain is an elementary divisor domain if and only if it is a duo-domain of neat range one.