Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-12-01T00:03:06.558Z Has data issue: false hasContentIssue false
  • English
  • Français

The decomposition of artinian modules over hyper-(cyclic or finite) groups

Published online by Cambridge University Press:  20 January 2009

Y. B. Qin
Y. B. Qin
Affiliation:
Department of Applying Mathematics Southwest China Communication University Chengdu 610031 P. R., China
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

If G is a hyperfinite locally soluble group and A an artinian ZG-module then Zaĭcev proved that A has an f-decomposition. For G being a hyper-(cyclic or finite) locally soluble group, Z. Y. Duan has shown that any periodic artinian ZG-module A has an f-decomposition. Here we prove that: if G is a hyper-(cyclic or finite) group, then any artinian ZG-module A has an f-decomposition.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 39 , Issue 1 , February 1996 , pp. 115 - 118
Copyright
Copyright © Edinburgh Mathematical Society 1996

References

REFERENCES

1. Duan, Z. Y., Noetherian modules over hyperfinite groups (Ph. D. Thesis, University of Glasgow, 1991).Google Scholar
2. Duan, Z. Y., Extensions of abelian by hyper-(cyclic or finite) groups 1, Comm. Algebra 20(8) (1992), 2305–2321.CrossRefGoogle Scholar
3. Duan, Z. Y., The f-decomposition of artinian modules over hyperfinite groups, to appear.Google Scholar
4. Jalegaonkar, A. V., Integral group rings of polycyclic-by-finite groups, J. Pure, Appl. Alg. 4 (1974), 337–343.CrossRefGoogle Scholar
5. Robinson, D. J. S., A Course in the Theory of Groups (Springer-Verlag, New York, 1982).CrossRefGoogle Scholar
6. Zaicev, D. I., Hypercyclic extensions of abelian groups, Akad. Nauk Ukrain. SSR, Inst. Mat. Kiev (1979), 16–37.Google Scholar
7. Zaicev, D. I., Splitting of extensions of abelian groups, Akad. Nauk Ukrain. SSR, Inst. Mat. Kiev( 1986), 21–31.Google Scholar