Modules Over Group Rings with Restrictions on Some Factor-Modules |
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| Authors: | Leonid?A.?Kurdachenkol,Marco?Trombetti mailto:marco.trombetti@unina.it" title=" marco.trombetti@unina.it" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author http://orcid.org/---" itemprop=" url" title=" View OrcID profile" target=" _blank" rel=" noopener" data-track=" click" data-track-action=" OrcID" data-track-label=" " >View author&# s OrcID profile |
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| Affiliation: | 1.Department of Algebra,National University of Dnepropetrovsk,Dnepropetrovsk,Ukraine;2.Dipartimento di Matematica e Applicazioni,Universit di Napoli Federico II Complesso Universitario Monte S. Angelo,Naples,Italy |
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| Abstract: | ![]()
Let D be a Dedekind domain and G be a group. In this paper we study DG-modules in which every proper factor-module, a part from the trivial one, is D-artinian. In particular, we prove that if such modules are not D-torsion-free, then their study can be traced back to the already known study of FG-modules (here F is a field) with each proper factor-module having finite F-dimension. Finally, we obtain a good picture of D-torsion-free, factorially D-artinian DG-modules, when G is a locally soluble FC-hypercentral group. |
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