Algebras and Representation Theory

, Volume 17, Issue 1, pp 87–102

On Modules Over Group Rings


DOI: 10.1007/s10468-012-9388-5

Cite this article as:
Tamer Koşan, M., Lee, TK. & Zhou, Y. Algebr Represent Theor (2014) 17: 87. doi:10.1007/s10468-012-9388-5


Let M be a right module over a ring R and let G be a group. The set MG of all formal finite sums of the form ∑ g ∈ Gmgg where mg ∈ M becomes a right module over the group ring RG under addition and scalar multiplication similar to the addition and multiplication of a group ring. In this paper, we study basic properties of the RG-module MG, and characterize module properties of (MG)RG in terms of properties of MR and G. Particularly, we prove the module-theoretic versions of several well-known results on group rings, including Maschke’s Theorem and the classical characterizations of right self-injective group rings and of von Neumann regular group rings.


Group ringGroup moduleMaschke’s TheoremSemisimple moduleRegular moduleInjective moduleFP-injective module

Mathematics Subject Classifications (2010)

Primary 16S34; Secondary 16D5016D6016E50

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.Department of MathematicsGebze Institute of TechnologyGebze/KocaeliTurkey
  2. 2.Department of MathematicsNational Taiwan UniversityTaipeiTaiwan
  3. 3.Department of Mathematics and StatisticsMemorial University of NewfoundlandSt.John’sCanada