On Submodules of Modules over Group Rings

Abstract

In this paper, we find some connections between submodules of a module over a group ring RG and subgroups of a group G. Also, we prove that there is a direct connection between conjugate elements of G and RG-submodules of M. Finaly, we show that there is a correspondence between the associative powers △_{M}^{i}(G)s of △_{M}(G) and ith dimension subgroups ▽(△_{R}^{i}(G)) of G over R.