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Semisimple classes of alternative rings

Published online by Cambridge University Press:  20 January 2009

T. Anderson  and
R. Wiegandt
T. Anderson
Affiliation:
Department of MathematicsUniversity of British ColumbiaVancouver, B.C., Canada
R. Wiegandt
Affiliation:
Mathematical InstituteHungarian Academy of ScienceRealtanoda u. 13–15H-1053 Budapest.
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Recently A. D. Sands [7] solved a problem posed in [6], and characterised the semisimple classes of associative rings as classes being regular, coinductive and closed under extensions. It is the purpose of this note to prove the same assertion for alternative rings. This result is perhaps not surprising, nevertheless its proof cannot be considered an easy one, and it requires a technique of dealing with ideals of ideals. In addition, semisimple classes of hereditary radicals and those of supernilpotent radicals will be characterised as easy consequences of our theorem.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 25 , Issue 1 , February 1982 , pp. 21 - 26
Copyright
Copyright © Edinburgh Mathematical Society 1982

References

REFERENCES

1.Anderson, T., Divinsky, N. and Suléinski, A., Hereditary radicals in associative and alternative rings, Canad. J. Math. 17 (1965), 594–603.CrossRefGoogle Scholar
2.Anderson, T. and Wiegandt, R., Weakly homomorphically closed semi-simple classes, Acta Math. Acad. Sci. Hungar. 34 (1979), 329–336.CrossRefGoogle Scholar
3.Leavitt, W. G., The general theory of radicals (Univ. of Nebraska, Lincoln, 1970).Google Scholar
4.Van Leeuwen, L. C. A., Properties of semisimple classes, J. Nat. Sci. & Math., Lahore 15 (1975), 59–67.Google Scholar
5.Van Leeuwen, L. C. A., Roos, C. and Wiegandt, R., Characterizations of semisimple classes, J. Austral. Math. Soc. (Series A) 23 (1977), 172–182.CrossRefGoogle Scholar
6.Van Leeuwen, L. C. A. and Wiegandt, R., Radicals, semisimple classes and torsion theories, Acta Math. Acad. Sci. Hungar. 36 (1980), 37–47.CrossRefGoogle Scholar
7.Sands, A. D., A characterization of semisimple classes, Math. Soc. (2) 24 (1981), 5–7.Google Scholar