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On the radical of a ring with minimum condition

Published online by Cambridge University Press:  09 April 2009

D. W. Barnes
D. W. Barnes
Affiliation:
The University of Sydney
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The purpose of this note is to establish the following characterisation of the radical: Theorem. Let R be a ring with the minimum condition for left ideals. Then the radical of R is the intersection of the maximal nilpotent subrings of R.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 5 , Issue 2 , May 1965 , pp. 234 - 236
Copyright
Copyright © Australian Mathematical Society 1965

References

[1]Artin, E., Nesbitt, C. J. and Thrall, R. M., Rings with minimum condition (University of Michigan Press, Ann Arbor, 1944).Google Scholar