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Hereditary Radicals in Associative and Alternative Rings

Published online by Cambridge University Press:  20 November 2018

T. Anderson ,
N. Divinsky  and
A. Suliński
T. Anderson
Affiliation:
University of British Columbia and Polish Academy of Sciences
N. Divinsky
Affiliation:
University of British Columbia and Polish Academy of Sciences
A. Suliński
Affiliation:
University of British Columbia and Polish Academy of Sciences
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In the first part of this paper we shall consider associative rings, pointing out where associativity is required. In the second part we shall consider not necessarily associative rings and in particular alternative rings.

A property S of rings is said to be a radical property, in the sense of Kurosh (4), if it satisfies the following three conditions:

(a) Every homomorphic image of an S-ring (i.e. a ring with property S) is again an S-ring.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 594 - 603
Copyright
Copyright © Canadian Mathematical Society 1965

References

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3. Kaplansky, I., Semi-simple alternative rings, Portugal. Math., 10 (1951), 37–50.Google Scholar
4. Kurosh, A., Radicals of rings and algebras, Math. Sb., 53 (1953), 13–26.Google Scholar
5. Smiley, M. F., An application of a radical of Brown and McCoy to non-associative rings, Amer. J. Math., 72 (1950), 93–100.Google Scholar