Hostname: page-component-5c6d5d7d68-lvtdw Total loading time: 0 Render date: 2024-08-18T12:29:37.955Z Has data issue: false hasContentIssue false
  • English
  • Français

Notes on a radical of Divinsky

Published online by Cambridge University Press:  20 January 2009

A. D. Sands
A. D. Sands
Affiliation:
Department of Mathematics and Computer ScienceUniversity of DundeeDundee, DD1 4HNScotland
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 his book [1] Divinsky refers to eight radicals as classical. In [6] radicals were considered such that the radical of each one-sided ideal of a ring may be expressed as the intersection of a left ideal and a right ideal of the ring. From results obtained there it was deduced that seven of these eight radicals have this property. The purpose of this note is to give a proof that this property also holds for the remaining one of these classical radicals.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 32 , Issue 1 , February 1989 , pp. 31 - 32
Copyright
Copyright © Edinburgh Mathematical Society 1989

References

REFERENCES

1.Divinsky, N. J., Rings and Radicals (Toronto University Press, Toronto, 1965).Google Scholar
2.Fuchs, L., Ringe und ihre additive Gruppe, Publ. Math. Debrecen 4 (1956), 488–508.CrossRefGoogle Scholar
3.Gardner, B. J., Some remarks on radicals of rings with chain conditions, Acta Math. Acad. Sci. Hungar. 25 (1974), 263–268.CrossRefGoogle Scholar
4.Jaegermann, M. and Sands, A. D., On normal radicals, N-radicals and A-radicals, J. Algebra 50 (1978), 337–349.CrossRefGoogle Scholar
5.Sands, A. D., On normal radicals, J. London Math. Soc. 11 (1975), 361–365.CrossRefGoogle Scholar
6.Sands, A. D., Radicals and one-sided ideals, Proc. Royal Soc. Edinburgh 103 (1986), 241–251.CrossRefGoogle Scholar