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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    Puczyłowski, E. R. 1993. On general theory of radicals. Algebra Universalis, Vol. 30, Issue. 1, p. 53.
    Veldsman, Stefan 1989. Sufficient conditions for a well-behaved Kurosh-Amitsur radical theory. Proceedings of the Edinburgh Mathematical Society, Vol. 32, Issue. 03, p. 377.
    Ánh, P.N. and Wiegandt, R. 1985. Semisimple classes of nonassociative rings and jordon algebras. Communications in Algebra, Vol. 13, Issue. 12, p. 2669.
    Ánh, P.N. Loi, N.V. and Wiegandt, R. 1985. On the radical theory of Andrunakievich varieties. Bulletin of the Australian Mathematical Society, Vol. 31, Issue. 02, p. 257.
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On semisimple classes of associative and alternative rings

  • E. R. Puczyłowski (a1)
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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.

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COPYRIGHT: © Edinburgh Mathematical Society 1984
References
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1.Anderson, T., Divinsky, N. and Sulinski, A., Hereditary radicals in associative and alternative rings, Canad. J. Math. 17 (1965), 594–603.
2.Anderson, T. and Wiegandt, R., Semisimple classes of alternative rings, Proc. Edinburgh Math. Soc. 25 (1982), 21–26.
3.Van Leeuwen, L. C. A., Roos, C. and Wiegandt, R., Characterizations of semisimple classes, Austral. Math. Soc. (Series A) 23 (1977), 172–182.
4.Puczylowski, E. R., Radicals of rings and their subrings, Proc. Edinburgh Math. Soc. 24 (1981), 209–215.
5.Rossa, R. F. and Tangeman, R. L., General heredity for radical theory, Proc. Edinburgh Math. Soc. 20 (1976/1977), 333–337.
6.Sands, A. D., Strong upper radicals,. Quart J. Math. (Oxford) 27 (1976), 21–24.
7.Sands, A. D., A characterization of semisimple classes, Proc. Edinburgh Math. Soc. 24 (1981), 5–7.
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.
9.Wiegandt, R., List of Problems, Kolloquium uber Algebra(Vienna, 1978), 6.
10.Wiegandt, R., Radical and semisimple classes of rings, (Queen's Papers in Pure and Applied Mathematics, No. 37, Kingston, Ontario, 1974).
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Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
  • URL: /core/journals/proceedings-of-the-edinburgh-mathematical-society
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