Artinian Modules over Group Rings [electronic resource] /
Kurdachenko, Leonid.author.
Otal, Javier.author.
Subbotin, Igor Ya.author.
Highlights developments on artinian modules over group rings of generalized nilpotent groups. This work includes traditional topics such as direct decompositions of artinian modules, criteria of complementability, and criteria of semisimplicity of artinian modules. It also allows a generalization of Maschke Theorem in classes of infinite groups.
Description based upon print version of record.
Highlights developments on artinian modules over group rings of generalized nilpotent groups. This work includes traditional topics such as direct decompositions of artinian modules, criteria of complementability, and criteria of semisimplicity of artinian modules. It also allows a generalization of Maschke Theorem in classes of infinite groups.
Includes bibliographical references (p. [227]-244) and index.
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.
Algebra.
Algebra.

Frontiers in Mathematics