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On special radicals, supernilpotent radicals and weakly homomorphically closed classes

Part of: Other nonassociative rings and algebras

Published online by Cambridge University Press:  09 April 2009

Ju. M. Rjabuhin  and
R. Wiegandt
Ju. M. Rjabuhin
Affiliation:
CCCP 27708, Кишинёв, ул. Академическая 5.
R. Wiegandt
Affiliation:
Mathematical Institute, Hungarian Academy of Sciences, Reáltanoda u. 13-15., H-1053 Budapest
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Abstract

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It is proved that a regular essentially closed and weakly homomorphically closed proper subclass of rings consists of semiprime rings. A regular class M defines a supernilpotent upper radical if and only if M consists of semiprime rings and the essential cover Mk of M is contained in the semisimple class S U M. A regular essentially closed class M containing all semisimple prime rings, defines a special upper radical if and only if M satisfies condition (S): every M-ring is a subdirect sum of prime M-rings. Thus we obtained a characterization of semisimple classes of special radicals; a subclas S of rings is the semisimple class of a special radical if and only if S is regular, subdirectly closed, essentially closed, and satisfies condition (S). The results are valid for alternative rings too.

Keywords

Kurosh-Amitsur radicalsupernilpotent radicalspecial radicalessentially and weakly homomorphically closed class.

MSC classification

Secondary: 17D05: Alternative rings
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 31 , Issue 2 , August 1981 , pp. 152 - 162
Copyright
Copyright © Australian Mathematical Society 1982

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