On modules over group rings of soluble groups with commutative ring of scalars

• Date: 2018
• Main Author: Dashkova, O. Yu.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: a maximal condition on subgroups; a Noetherian module; a soluble group; 20F16; 20H25
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/650
• Journal Title: Algebra and Discrete Mathematics

The author studies an \(\bf R\)\(G\)-module \(A\) such that \(\bf R\) is a commutative ring, \(A/C_{A}(G)\) is not a Noetherian \(\bf R\)-module,  \(C_{G}(A)=1\), \(G\) is a soluble group. The system of all subgroups \(H \leq G\), for which the quotient modules \(A/C_{A}(H)\) are not Noetherian  \(\...