On modules with few minimax cocentralizers

TL;DR

This paper investigates modules over a ring with a focus on those where the quotient by centralizers of certain subgroups exhibits minimax properties, advancing understanding of module structure relative to subgroup actions.

Contribution

It introduces a new class of modules characterized by minimax quotients over centralizers of non-finitely generated subgroups, expanding the theory of module and group interactions.

Findings

Characterization of modules with minimax quotients over subgroup centralizers

Identification of conditions under which modules exhibit minimax properties

Extension of minimax module theory to group actions on modules

Abstract

Let R be a ring and G a group. An R-module A is said to be minimax if A includes an noetherian submodule B such that A=B is artinian. The authors study a ZG-module A such that A/C_A(H) is minimax (as a Z-module) for every proper not finitely generated subgroup H.