Artinian Modules over Group Rings (Frontiers in Mathematics) - Brossura

Kurdachenko, Leonid A.

Brossura

ISBN 10: 376437764X ISBN 13: 9783764377649

Casa editrice: Birkhäuser Basel, 2006

Riassunto

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. As self-contained as possible, this book will be useful for students as well as for experts in group theory, ring theory, and module theory.

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Recensione

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)

Contenuti

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.

Dettagli dell'edizione

• Editore: Birkhäuser Basel
• Data di pubblicazione: 2006
• Lingua: Inglese
• ISBN 10: 376437764X
• ISBN 13: 9783764377649
• Rilegatura: Copertina flessibile
• Numero di pagine: 264
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile