Artinian Modules over Group Rings

• Modules with chain conditions.- Ranks of groups.- Some generalized nilpotent groups.- Artinian modules and the socle.- Reduction to subgroups of finite index.- Modules over Dedekind domains.- The Kovacs-Newman theorem.- Hartley’s classes of modules.- The injectivity of some simple modules.- Direct decompositions in artinian modules.- On the countability of artinian modules over FC-hypercentral groups.- Artinian modules over periodic abelian groups.- Nearly injective modules.- Artinian modules over abelian groups of finite section rank.- The injective envelopes of simple modules over group rings.- Quasifinite modules.- Some applications: splitting over the locally nilpotent residual.

From the reviews: "The theory of modules over group rings RG for infinite groups G over arbitrary rings R is a very extensive and complex field of research with a great number of scattered results. ... Since many of the results appear for the first time in a book it can be recommended warmly to any expert in this field, but also for graduate students who are presented the beauty of the interplay of the theories of groups, rings and representations." (G. Kowol, Monatshefte fur Mathematik, Vol. 152 (4), December, 2007)