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- Title
On Modules Over Group Rings.
- Authors
Tamer Koşan, M.; Lee, Tsiu-Kwen; Zhou, Yiqiang
- 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 ∑ m g where m ∈ 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) in terms of properties of M 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.
- Publication
Algebras & Representation Theory, 2014, Vol 17, Issue 1, p87
- ISSN
1386-923X
- Publication type
Article
- DOI
10.1007/s10468-012-9388-5