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Unequivocal Rings

Published online by Cambridge University Press:  20 November 2018

N. Divinsky
N. Divinsky*
Affiliation:
University of British Columbia, Vancouver, British Columbia; University of London-Queen Mary College, London, England
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For any radical property Q, a nonzero simple ring (all rings in this paper are assumed to be associative) must make up its mind so to speak and must be either Q radical or Q semi-simple. Every Q thus divides the class of all nonzero simple rings into two disjoint classes. Conversely any partition of the nonzero simple rings into two disjoint classes leads to at least two radicals [1, p. 16].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 3 , 01 June 1975 , pp. 679 - 690
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Divinsky, N., Rings and radicals (Univ. of Toronto Press, Toronto, 1965).Google Scholar
2. Divinsky, N., Duality between radical and semi-simple classes of associative rings, Scripta Math. 29 (1973), 409–416.Google Scholar
3. Fuchs, L., Abelian groups (Pergamon Press, New York, 1960).Google Scholar
4. Gardner, B. J., Some remarks on radicals of rings with chain conditions, U. of Tasmania Technical Report #4, March, 1972.Google Scholar
5. Hoffman, A. E. and Leavitt, W. G., Properties inherited by the lower radical, Portugal. Math. 27 (1968), 63–66.Google Scholar
6. Johnson, R. E., Equivalence rings, Duke Math. J. 15 (1948), 787–793.Google Scholar
7. Lee, Y. L., On the construction of lower radical properties, Pacific J. Math. 28 (1969), 393–395.Google Scholar
8. Sulinski, A., Anderson, T., and Divinsky, N., Lower radical properties for associative and alternative rings, J. London Math. Soc. 41 (1966), 417–424.Google Scholar
9. Wolfson, K. G., An ideal-theoretic characterization of the ring of all linear transformations, Amer. J. Math. 75 (1953), 358–386.Google Scholar