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Radicals and one-sided ideals

Published online by Cambridge University Press:  14 November 2011

A.D. Sands
A.D. Sands
Affiliation:
Department of Mathematical Sciences, The University, Dundee, DD1 4HN, U.K.
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Extract

The correspondence between radicals of associative rings and A-radicals is studied. It is shown that corresponding to each A-radical there is an interval of radicals and that each radical belongs to exactly one such interval. The question of the nature of the radical of a one-sided ideal is considered. It is shown that the radicals such that the radical of a one-sided ideal is always a one-sided ideal are those which contain their associated A-radicals. Radicals such that the radical of a one-sided ideal always equals the intersection of a left ideal and a right ideal are described, as are those A-radicals such that every associated radical has this property.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 103 , Issue 3-4 , 1986 , pp. 241 - 251
Copyright
Copyright © Royal Society of Edinburgh 1986

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