\(F\)-supplemented modules

• Date: 2020
• Main Author: Özdemir, S.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2020
• Subjects: \(F\)-supplement and \(F\)-small submodules; \(F\)-supplemented; \(F\)-local and \(F\)-hollow modules; 16D10; 16D80
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1185
• Journal Title: Algebra and Discrete Mathematics

Let \(R\) be a ring, let \(M\) be a left \(R\)-module, and let \(U, V, F\) be submodules of \(M\) with \(F\) proper. We call \(V\) an \(F\)-supplement of \(U\) in \(M\) if \(V\) is minimal in the set \( F \subseteq X \subseteq M\) such that \( U + X = M\), or equivalently, \(F\subseteq V\), \(U + V...