Hostname: page-component-7bb8b95d7b-pwrkn Total loading time: 0 Render date: 2024-09-16T13:38:44.387Z Has data issue: false hasContentIssue false
  • English
  • Français

Quasi-Frobenius quotient rings of group rings

Published online by Cambridge University Press:  09 April 2009

Andreas Horn
Andreas Horn
Affiliation:
Mathematisches Institut Justus-Liebig-Universität63 Giessen Arndtstr. 2, West Germany
Rights & Permissions [Opens in a new window]

Extract

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.

The purpose of this paper is an extension of a theorem of Hughes (1973). He showed: Let R be a ring which has a right artinian right quotient ring and let G be a group which has a (transfinite) ascending normal series with each factor either finite or cyclic, but only a finite number of finite factors. Then the group ring RG has a right artinian right quotient ring.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 20 , Issue 4 , November 1975 , pp. 394 - 397
Copyright
Copyright © Australian Mathematical Society 1975

References

Hajarnavis, C. R. (1971), ‘Orders in QF and QF 2 rings’, J. Algebra 19, 329–343.CrossRefGoogle Scholar
Horn, A. (1973), ‘Gruppenringe fastpolyzyklischer Gruppen und Ordnungen in Quasi-Frobenius-Ringen’, Mitt. Math. Sem. Giessen 100.Google Scholar
Hughes, I. (1973), ‘Artinian quotient rings of group rings’, J. Austral. Math. Soc. 16, 379–384.CrossRefGoogle Scholar
Kurosh, A. (1956), The Theory of Groups, Vol. 2 (Chelsea, New York, 1956).Google Scholar
Shock, R. C. (1972), ‘Polynomial rings over finite dimensional rings’, Pacific J. Math. 42, 251–257.CrossRefGoogle Scholar
Small, L. W. (1966), ‘Orders in Artinian rings’, J. Algebra 4, 13–41.CrossRefGoogle Scholar