\(F\)-supplemented modules

• Дата: 2020
• Автор: Özdemir, S.
• Формат: Стаття
• Мова: English
• Опубліковано: Lugansk National Taras Shevchenko University 2020
• Теми: \(F\)-supplement and \(F\)-small submodules; \(F\)-supplemented; \(F\)-local and \(F\)-hollow modules; 16D10; 16D80
• Онлайн доступ: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1185
• Назва журналу: 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, \(F\subseteq V\), \(U + V = M\) and \(U \cap V \) is \(F\)-small in \( V\). If every submodule of \(M\) has an \(F\)-supplement, then we call \(M\) an \(F\)-supplemented module. In this paper, we introduce and investigate \(F\)-supplement submodules and (amply) \(F\)-supplemented modules. We give some properties of these modules, and characterize finitely generated (amply) \(F\)-supplemented modules in terms of their certain submodules.