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

Abstract

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  \(\bf R\)-modules, satisfies the maximal  condition. This condition  is called the condition \(max-nnd\). The structure of the group \(G\) is described.