On modules over group rings
Journal
Algebras and Representation Theory
Journal Volume
17
Journal Issue
1
Pages
87-102
Date Issued
2014
Author(s)
Abstract
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 Σ g *̂ G m g g where m g *̂ 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 M R 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. © 2012 Springer Science+Business Media Dordrecht.
Type
journal article