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Journals / Turkish Journal of Mathematics / 2014 / Cilt: 38 - Sayı: 1

On the structure of some modules over generalized soluble groups

Leonid Andreevich KURDACHENKO, Igor Yakov SUBBOTIN, Vasiliy Anatolievich CHUPORDYA

Pages
52–59
DOI
—

Abstract

Let R be a ring and G a group. An R-module A is said to be Artinian-by-(finite rank) if TorR(A) is Artinian and A/ TorR(A) has finite R-rank. We study a module A over a group ring RG such that A/CA(H) is Artinian-by-(finite rank) (as an R-module) for every proper subgroup H.

Özet

Let R be a ring and G a group. An R-module A is said to be Artinian-by-(finite rank) if TorR(A) is Artinian and A/ TorR(A) has finite R-rank. We study a module A over a group ring RG such that A/CA(H) is Artinian-by-(finite rank) (as an R-module) for every proper subgroup H.

Keywords: Modules, group rings, modules over group rings, generalized soluble groups, radical groups, Artinian modules, generalized radical groups, modules of finite rank