Artinian Modules over Group Rings

By: Leonid Kurdachenko, Javier Otal, Igor Ya Subbotin

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Paperback | 23 October 2006

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260 Pages

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23.5 x 16.51 x 1.91

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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. The theory of modules over groups has its own specific character that plays an imperative role here and, for example, allows a significant generalization of the classical Maschke Theorem on some classes of infinite groups. Conversely, it leads to establishing direct decompositions of artinian modules related to important natural formations, which, in turn, find very efficient applications in infinite groups.

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"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 fuer Mathematik, Vol. 152 (4), December, 2007)

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Preface	p. ix
Modules with chain conditions	p. 1
Ranks of groups	p. 13
Some generalized nilpotent groups	p. 25
Artinian modules and the socle	p. 37
Reduction to subgroups of finite index	p. 45
Modules over Dedekind domains	p. 53
The Kovacs-Newman theorem	p. 63
Hartley's classes of modules	p. 81
The injectivity of some simple modules	p. 93
Direct decompositions in artinian modules	p. 111
On the countability of artinian modules over FC-hypercentral groups	p. 131
Artinian modules over periodic abelian groups	p. 153
Nearly injective modules	p. 161
Artinian modules over abelian groups of finite section rank	p. 167
The injective envelopes of simple modules over group rings	p. 179
Quasifinite modules	p. 189
Some applications: splitting over the locally nilpotent residual	p. 211
Bibliography	p. 227
Index	p. 245
Table of Contents provided by Ingram. All Rights Reserved.

Artinian Modules over Group Rings

At a Glance

Paperback

Industry Reviews

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How to return your order

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