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Sufficient conditions for a well-behaved Kurosh-Amitsur radical theory

Published online by Cambridge University Press:  20 January 2009

Stefan Veldsman
Stefan Veldsman
Affiliation:
Department of MathematicsUniversity of Port ElizabethP.O. Box 16006000 Port Elizabeth, South Africa
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Kurosh-Amitsur radical theories have been developed for various algebraic structures. Whenever the notion of a normal substructure is not transitive, this causes quite some problems in obtaining satisfactory general results. Some of the more important questions concerning the general theory of radicals are whether semisimple classes are hereditary, do radical classes satisfy the ADS-property, can semisimple classes be characterized by closure conditions (e.g., is semisimple=coradical), is Sands' Theorem valid and lastly, does the lower radical construction terminate. For associative and alternative rings, all these questions have positive answers. The method of proof is the same in both cases. In [15], Puczylowski used the results of Terlikowska-Oslowska [18, 19] and hinted at a condition which is crucial in obtaining the positive answers to the above questions.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 32 , Issue 3 , October 1989 , pp. 377 - 394
Copyright
Copyright © Edinburgh Mathematical Society 1989

References

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