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.
Modules Over Group Rings with Restrictions on Some Factor-Modules / Kurdachenkol, Leonid A.; Trombetti, Marco. - In: MEDITERRANEAN JOURNAL OF MATHEMATICS. - ISSN 1660-5446. - 14:3(2017). [10.1007/s00009-017-0937-3]
Modules Over Group Rings with Restrictions on Some Factor-Modules
Trombetti, Marco
2017
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.| File | Dimensione | Formato | |
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L.A. Kurdachenko & M.T. - Modules over group rings with restrictions on some factor-modules.pdf
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