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A Note on the Jacobson And Brown-McCoy Radicals

Published online by Cambridge University Press:  20 November 2018

T. Anderson  and
A. Heinicke
T. Anderson
Affiliation:
The University of British Columbia
A. Heinicke
Affiliation:
The University of British Columbia
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Let J(R) and G(R) respectively denote the Jacobson and Brown-McCoy radicals of the ring R and recall that R = G(R) if and only if R can not be homomorphically mapped onto a simple ring with unity [1, p. 120].

In general one knows that J(R) ⊆ G(R) [1, p. 118], while there do exist rings R for which J(R) ≠ G(R) (see [1, p. 120]).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 5 , December 1968 , pp. 737 - 738
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Divinsky, N.J., Rings and radicals. (University of Toronto Press, 1965).Google Scholar
2. Jacobson, N., Structure of rings. Amer. Math. Soc. Coll. Publ. 37 (1956).Google Scholar
3. Sasiada, E. and Sulinski, A., A note on the Jacobson radical. Bull. Acad. Polon. Sci. 10 (1962) 421-423.Google Scholar