Flexible modules and graded rings

Abstract

A G−graded R−module is called flexible if Mg = RgMe for every g ∈ G. In this paper, we study the relationship between a flexible module and the graded ring R through different aspects. On one hand, we distinguish the flexible modules from other graded modules by characterizing the influence of the e-component of a flexible module on the graded module itself. On the other hand, we extend the class covered by flexible graded modules to include free and projective modules in a comparatively simple manner.