On semisimple classes of associative and alternative rings

Author:

Puczyłowski E. R.

Abstract

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.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference10 articles.

1. STRONG UPPER RADICALS

2. Semisimple classes of alternative rings

3. Characterizations of semisimple classes

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1. On general theory of radicals;Algebra Universalis;1993-03

2. Sufficient conditions for a well-behaved Kurosh-Amitsur radical theory;Proceedings of the Edinburgh Mathematical Society;1989-10

3. General Heredity and Strength for Radical Classes;Canadian Journal of Mathematics;1988-12-01

4. On the radical theory of Andrunakievich varieties;Bulletin of the Australian Mathematical Society;1985-04

5. Semisimple classes of nonassociative rings and jordon algebras;Communications in Algebra;1985-01

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