A Generalization of Group-Graded Modules

Abstract

In this article, we generalize the concept of group-graded modules by introducing the concept of G-weak graded R-modules, which are R-modules graded by a set G of left coset representatives, where R is a G-weak graded ring. Moreover, we prove some properties of these modules. Finally, results related to G-weak graded fields and their vector spaces are deduced. Many considerable examples are provided with more emphasis on the symmetric group S3 and the dihedral group D6, which gives the group of symmetries of a regular hexagon.