Artinian Modules over Group Rings [Paperback]

This book highlights important developments on artinian modules over group rings of generalized nilpotent groups. Along with traditional topics such as direct decompositions of artinian modules, criteria of complementability for some important modules, and criteria of semisimplicity of artinian modules, it also focuses on recent advanced results on these matters.

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.- Hartleys 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 f?r Mathematik, Vol. 152 (4), December, 2007)

First book focussing on artinian modules

While usually the investigation of a corresponding ring structure precedes the study of a module over this ring, the book implements module properties through the artinian condition

This book highlights important developments on artinian modules over group rings of generalized nilplã)