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. Finally, we show that there is a correspondence between the associative powers ?iM(G) of ?M(G) and ith dimension subgroups ?(?i R(G)) of G over R.