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Characterizations of semisimple classes

Published online by Cambridge University Press:  09 April 2009

L. C. A. van Leeuwen ,
C. Roos  and
R. Wiegandt
L. C. A. van Leeuwen
Affiliation:
Department of Mathematics, The University of Groningen, Groningen, The Netherlands.
C. Roos
Affiliation:
Department of Mathematics, Institute of Technology, Delft, The Netherlands.
R. Wiegandt
Affiliation:
Mathematical Institute of the Hung. Acad. of Sci., Reáltanoda u. 13–15, H-1053 Budapest, Hungary.
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Abstract

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Two characterizations of semisimple classes of associative and alternative rings (and semigroups with 0) are given:

(i) A class is a semisimple class if and only if it is hereditary, closed under extensions and subdirect sums;

(ii) A class is a semisimple class if and only if it is hereditary, closed under extensions, and has the co-inductive property.

The first characterization sharpens Armendariz's (1968) result proved for associative rings, the second one is categorically dual to a characterization of radical classes due to Amitsur (1954).

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 23 , Issue 2 , March 1977 , pp. 172 - 182
Copyright
Copyright © Australian Mathematical Society 1977

References

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