Amply (weakly) Goldie-Rad-supplemented modules

• Date: 2016
• Main Author: Takıl Mutlu, Figen
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2016
• Subjects: Supplement submodule; Goldie-Rad-Supplement submodule; amply Goldie-Rad-Supplemented module; 16D10; 16D40; 16D70
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/59
• Journal Title: Algebra and Discrete Mathematics

Let \(R\) be a ring and \(M\) be a right \(R\)-module. We say a submodule \(S\) of \(M\) is a \textit{(weak) Goldie-Rad-supplement} of a submodule \(N\) in \(M\), if \(M=N+S\), \((N\cap S \leq Rad(M))\) \(N\cap S\leq Rad(S)\) and \(N\beta^{**} S\), and  \(M\) is called amply (weakly) Goldie-Rad-supp...