On lifting and extending properties on direct sums of hollow uniform modules

• Date: 2022
• Main Author: Shibata, Y.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2022
• Subjects: lifting modules; extending modules; finite internal exchange property; 16D40; 16D70
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1643
• Journal Title: Algebra and Discrete Mathematics

A module \(M\) is said to be lifting if, for any submodule \(N\) of \(M\), there exists a direct summand \(X\) of \(M\) contained in \(N\) such that \(N/X\) is small in \(M/X\). A module \(M\) is said to satisfy the {\it finite internal exchange property} if, for any direct summand \(X\) of \(M\) an...