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On prime essential rings

Published online by Cambridge University Press:  17 April 2009

Halina France-Jackson
Halina France-Jackson
Affiliation:
Department of Mathematics, Vista University, Port Elizabeth 6000, South Africa
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Abstract

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A ring A is prime essential if A is semiprime and every prime ideal of A has a nonzero intersection with each nonzero ideal of A. We prove that any radical (other than the Baer's lower radical) whose semisimple class contains all prime essential rings is not special. This yields non-speciality of certain known radicals and answers some open questions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 47 , Issue 2 , April 1993 , pp. 287 - 290
Copyright
Copyright © Australian Mathematical Society 1993

References

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