On the direct sum of dual-square-free modules

• Date: 2022
• Main Authors: Ibrahim, Y., Yousif, M.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2022
• Subjects: square-free and dual-square-free modules; abelian and quasi-duo rings; Primary 16D40; 16D50; 16D60; Secondary 16L30; 16L60; 16P20; 16P40; 16P60
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1807
• Journal Title: Algebra and Discrete Mathematics

A module \(M\) is called square-free if it contains no non-zero isomorphic submodules \(A\) and \(B\) with \(A \cap B =0\). Dually, \(M\) is called dual-square-free if \(M\) has no proper submodules \(A\) and \(B\) with \(M =A +B\) and \(M/A \cong M/B\). In this paper we show that if \(M = \oplus _{...