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Artinian Modules Over Group Rings : Frontiers in Mathematics - Leonid A. Kurdachenko

Artinian Modules Over Group Rings

Frontiers in Mathematics

Paperback

Published: 23rd October 2006
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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.

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)

Prefacep. ix
Modules with chain conditionsp. 1
Ranks of groupsp. 13
Some generalized nilpotent groupsp. 25
Artinian modules and the soclep. 37
Reduction to subgroups of finite indexp. 45
Modules over Dedekind domainsp. 53
The Kovacs-Newman theoremp. 63
Hartley's classes of modulesp. 81
The injectivity of some simple modulesp. 93
Direct decompositions in artinian modulesp. 111
On the countability of artinian modules over FC-hypercentral groupsp. 131
Artinian modules over periodic abelian groupsp. 153
Nearly injective modulesp. 161
Artinian modules over abelian groups of finite section rankp. 167
The injective envelopes of simple modules over group ringsp. 179
Quasifinite modulesp. 189
Some applications: splitting over the locally nilpotent residualp. 211
Bibliographyp. 227
Indexp. 245
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9783764377649
ISBN-10: 376437764X
Series: Frontiers in Mathematics
Audience: General
Format: Paperback
Language: English
Number Of Pages: 247
Published: 23rd October 2006
Publisher: Birkhauser Verlag AG
Country of Publication: CH
Dimensions (cm): 23.98 x 17.12  x 1.35
Weight (kg): 0.49