Artinian Modules over Group Rings

Erscheinungsjahr 2006
ISBN: 978-3-7643-7764-9
Verlag: Springer

Buch, Englisch, 247 Seiten, Format (B × H): 170 mm x 244 mm, Gewicht: 930 g

Reihe: Frontiers in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Kurdachenko, Leonid

Otal, Javier

Subbotin, Igor Ya

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Algebra Elementare Algebra

Inhaltsverzeichnis

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.