Hostname: page-component-76dd75c94c-qmf6w Total loading time: 0 Render date: 2024-04-30T09:13:02.448Z Has data issue: false hasContentIssue false
  • English
  • Français

On Relations among radical properties

Published online by Cambridge University Press:  18 May 2009

A. D. Sands
A. D. Sands
Affiliation:
Department of Mathematics, The University Dundee, DD14HN, Scotland
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.

In this paper we work in the class of associative rings. The fundamental definitions and properties of radicals may be found in Divinsky [1].If α is a radical class of rings we shall denote the class of semi-simple rings by the radical of a ring R we shall denote by α(R).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 18 , Issue 1 , January 1977 , pp. 17 - 23
Copyright
Copyright © Glasgow Mathematical Journal Trust 1977

References

REFERENCES

1.Divinsky, N. J., Rings and radicals (Allen and Unwin, 1965).Google Scholar
2.Divinsky, N. J., Krempa, J. and Sulinski, A., Strong radical properties of alternative and associative rings, J. Algebra 17 (1971), 369–388.CrossRefGoogle Scholar
3.Hoffman, A. E. and Leavitt, W. G., Properties inherited by the lower radical, Portugal Math. 27 (1968), 63–66.Google Scholar
4.Krempa, J., Radicals of semi-group rings, Fund Math. 85 (1974), 57–71.CrossRefGoogle Scholar
5.Leavitt, W. G., Lower radical constructions, Colloq. Math. Soc. Janos Bolyai 6 (1973), 319–324.Google Scholar
6.Rossa, R. F., More properties inherited by the lower radical, Proc. Amer. Math. Soc. 33 (1972), 247–249.CrossRefGoogle Scholar
7.Sands, A. D., Radicals and Morita contexts, J. Algebra 24 (1973), 335–345.CrossRefGoogle Scholar
8.Sands, A. D., Strong upper radicals, Quart. J. Math. Oxford (2) 27 (1976), 21–24.CrossRefGoogle Scholar