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Unequivocal Rings

  • N. Divinsky (a1)

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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].

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References

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1. Divinsky, N., Rings and radicals (Univ. of Toronto Press, Toronto, 1965).
2. Divinsky, N., Duality between radical and semi-simple classes of associative rings, Scripta Math. 29 (1973), 409416.
3. Fuchs, L., Abelian groups (Pergamon Press, New York, 1960).
4. Gardner, B. J., Some remarks on radicals of rings with chain conditions, U. of Tasmania Technical Report #4, March, 1972.
5. Hoffman, A. E. and Leavitt, W. G., Properties inherited by the lower radical, Portugal. Math. 27 (1968), 6366.
6. Johnson, R. E., Equivalence rings, Duke Math. J. 15 (1948), 787793.
7. Lee, Y. L., On the construction of lower radical properties, Pacific J. Math. 28 (1969), 393395.
8. Sulinski, A., Anderson, T., and Divinsky, N., Lower radical properties for associative and alternative rings, J. London Math. Soc. 41 (1966), 417424.
9. Wolfson, K. G., An ideal-theoretic characterization of the ring of all linear transformations, Amer. J. Math. 75 (1953), 358386.
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Unequivocal Rings

  • N. Divinsky (a1)

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