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Some radical constructions for associative rings

Published online by Cambridge University Press:  09 April 2009

B. J. Gardner
B. J. Gardner
Affiliation:
Department of MathematicsInstitute of Advanced Studies, Australian National University, Canberra, ACT.
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Dickson's construction [1] of radical and semi-simple classes for certain abelian categories is a rather straightforward procedure in comparison with the methods traditionally used in more general situations. In §2 of the present paper we use a well-known characterization of the lower radical class to obtain, via consideration of maps with accessible images, a similar “homomorphic orthogonality” characterization of radical and semi-simple classes of associative rings. By substituting certain other subring properties for accessibility, we are then able to obtain simple constructions of various types of radical classes, including those which are strict in the sense first used by Kurosh [3] for groups.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 18 , Issue 4 , December 1974 , pp. 442 - 446
Copyright
Copyright © Australian Mathematical Society 1974

References

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