Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-24T12:35:57.909Z Has data issue: false hasContentIssue false
  • English
  • Français

On semisimple classes of associative and alternative rings

Published online by Cambridge University Press:  20 January 2009

E. R. Puczyłowski
E. R. Puczyłowski
Affiliation:
Institute of Mathematics University, Pkin, 00-901 Warsaw
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In [6] Sands proved that the semisimple classes of associative rings are exactly the coinductive and closed under ideals and extensions classes. This characterization was transferred to the alternative case by Van Leeuwen, Roos and Wiegandt in [3]. Answering a question of [9], Sands [7] has recently proved that in the associative case the condition of being closed under ideals can be replaced by the regularity of the class. The same result for alternative rings has been proved by Anderson and Wiegandt in [2]. Thus the following result holds.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 27 , Issue 1 , February 1984 , pp. 1 - 5
Copyright
Copyright © Edinburgh Mathematical Society 1984

References

REFERENCES

1.Anderson, T., Divinsky, N. and Sulinski, A., Hereditary radicals in associative and alternative rings, Canad. J. Math. 17 (1965), 594–603.CrossRefGoogle Scholar
2.Anderson, T. and Wiegandt, R., Semisimple classes of alternative rings, Proc. Edinburgh Math. Soc. 25 (1982), 21–26.CrossRefGoogle Scholar
3.Van Leeuwen, L. C. A., Roos, C. and Wiegandt, R., Characterizations of semisimple classes, Austral. Math. Soc. (Series A) 23 (1977), 172–182.CrossRefGoogle Scholar
4.Puczylowski, E. R., Radicals of rings and their subrings, Proc. Edinburgh Math. Soc. 24 (1981), 209–215.CrossRefGoogle Scholar
5.Rossa, R. F. and Tangeman, R. L., General heredity for radical theory, Proc. Edinburgh Math. Soc. 20 (1976/1977), 333–337.CrossRefGoogle Scholar
6.Sands, A. D., Strong upper radicals,. Quart J. Math. (Oxford) 27 (1976), 21–24.CrossRefGoogle Scholar
7.Sands, A. D., A characterization of semisimple classes, Proc. Edinburgh Math. Soc. 24 (1981), 5–7.CrossRefGoogle Scholar
8.Teruxowska-Ostowska, B., Category with a self-dual set of axioms, Bull. Acad. Polon. Sci., Ser. Sci. Math. Astronom. Phys. 25 (1977), 1207–1214.Google Scholar
9.Wiegandt, R., List of Problems, Kolloquium uber Algebra(Vienna, 1978), 6.Google Scholar
10.Wiegandt, R., Radical and semisimple classes of rings, (Queen's Papers in Pure and Applied Mathematics, No. 37, Kingston, Ontario, 1974).Google Scholar