RESEARCH ARTICLE

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

O. Yu. Dashkova

49010, Ukraine, Dniepropetrovsk, prospekt Gagarina, 72, Dniepropetrovsk National University, Department of Mathematics and Mechanics

Abstract: The author studies an $\mathbf RG$-module $A$ such that $\mathbf R$ is a commutative ring, $A/C_{A}(G)$ is not a Noetherian $\mathbf R$-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 $\mathbf R$-modules, satisfies the maximal condition. This condition is called the condition max–nnd. The structure of the group $G$ is described.

Keywords: a maximal condition on subgroups, a Noetherian module, a soluble group.

MSC: 20F16, 20H25

Language: English

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