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General Radicals that Coincide with the Classical Radical on Rings with D.C.C.

Published online by Cambridge University Press:  20 November 2018

N. Divinsky
N. Divinsky*
Affiliation:
University of British Columbia
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General radical theories were obtained by Amitsur (1; 2; 3) and Kurosh (6). Following Kurosh we say that a property of rings is a radical property if:

(a) Every homomorphic image of an -ring is an -ring;

(b) Every ring R contains an -ideal S which contains every other -ideal of R;

(c) The factor ring R/S is-semi-simple (that is, has no non-zero -ideals).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 13 , 1961 , pp. 639 - 644
Copyright
Copyright © Canadian Mathematical Society 1961

References

1. Amitsur, S. A., A general theory of radicals, Amer. J. Math., 74 (1952), 774–786.Google Scholar
2. Amitsur, S. A., A general theory of radicals II, Amer. J. Math., 76 (1954), 100–125.Google Scholar
3. Amitsur, S. A., A general theory of radicals III, Amer. J. Math., 76 (1954), 126–136.Google Scholar
4. Nesbitt, Artin, and Thrall, , Rings with minimum conditions. University of Michigan, publ. no. 1 (1946).Google Scholar
5. Baer, R., Radical ideals, Amer. J. Math. 65 (1943), 537–567.Google Scholar
6. Kurosh, A. G., Radicals of rings and algebras, Math. Sbornik, V, 33 (75) (1953).Google Scholar