Modules Over Group Rings with Restrictions on Some Factor-Modules

被引：1

作者：

Kurdachenkol, Leonid A. ^{[1
]}

Trombetti, Marco ^{[2
]}

机构：

[1] Natl Univ Dnepropetrovsk, Dept Algebra, Gagarin Prospect 72, UA-49010 Dnepropetrovsk, Ukraine

[2] Univ Napoli Federico II, Dipartimento Matemat & Applicaz, Complesso Univ Monte S Angelo,Via Cintia, Naples, Italy

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2017年 / 14卷 / 03期

关键词：

Factorially artinian module; Dedekind domain;

D O I：

10.1007/s00009-017-0937-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：11

共 11 条

[1] HARTLEY B, 1977, P LOND MATH SOC, V35, P55
[2] Karpilovsky Gregory., 1988, Field theory
[3] Kurdachenko L. A., 2002, GROUPS PRESCRIBED QU
[4] Kurdachenko L. A., JUST NONART IN PRESS
[5] Kurdachenko L. A., 2008, INSIGHT MODULES OVER
[6] Kurdachenko L. A., 2007, ARTINIAN MODULES OVE
[7] Kurdachenko L. A., 2003, SE ASIAN B MATH, V26, P773
[8] ON SOME TYPES OF NOETHERIAN MODULES
Kurdachenko, Leonid A.
Subbotin, Igor Ya.
[J]. JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2004, 3 (02) : 169 - 179
[9] Passman D. S., 1977, Pure and Applied Mathe- matics
[10] Passman D. S., 1984, GROUP THEORY ESSAYS, P207

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