Modules over some group rings having d-generator property

TL;DR

This paper introduces a new numerical parameter for modules over group rings, called the finite r-generator property, and characterizes modules over group algebras of finite groups that possess this property.

Contribution

It defines the finite r-generator property for modules over group rings and provides a description of modules over group algebras of finite groups with this property.

Findings

Characterization of modules with finite r-generator property over group algebras

Introduction of a new numerical parameter for modules over group rings

Description of modules over finite group algebras with the finite r-generator property

Abstract

For modules over group rings we introduce the following numerical parameter. We say that a module A over a ring R has finite r-generator property if each f.g. (finitely generated) R-submodule of A can be generated exactly by r elements and there exists a f.g. R-submodule D of A, which has a minimal generating subset, consisting exactly of r elements. Let FG be the group algebra of a finite group G over a field F. In the present paper modules over the algebra FG having finite generator property are described.