Artinian Modules over Group Rings
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Beschreibung
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.
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 Includes supplementary material: sn.pub/extras
Autor*in
Leonid Kurdachenko
Themen in »Artinian Modules over Group Rings«
Abelian group Artinian module DEX Finite boundary element method development finite group form group group ring group theory nilpotent group ring ring theory theorem
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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 für Mathematik, Vol. 152 (4), December, 2007)
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