Characterizations of semisimple classes-Reference-Cited by-同舟云学术

Characterizations of semisimple classes

Published:1977-03 Issue:2 Volume:23 Page:172-182
ISSN:1446-7887
Container-title:Journal of the Australian Mathematical Society
language:en
Short-container-title:J. Aust. Math. Soc.

Author:

van Leeuwen L. C. A.,Roos C.,Wiegandt R.

Abstract

AbstractTwo characterizations of semisimple classes of associative and alternative rings (and semigroups with 0) are given:(i) A class is a semisimple class if and only if it is hereditary, closed under extensions and subdirect sums;(ii) A class is a semisimple class if and only if it is hereditary, closed under extensions, and has the co-inductive property.The first characterization sharpens Armendariz's (1968) result proved for associative rings, the second one is categorically dual to a characterization of radical classes due to Amitsur (1954).

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference15 articles.

1. On the structure of lower radical semigroups;Wiegandt;Czechoslovak Math. J.,1972

2. A radical coinciding with the lower radical in associative and alternative rings

3. To the theory of radicals for semigroups;Grigor;II., Mat. Issled.,1973

4. On lower radicals of semigroups

5. A General Theory of Radicals. II. Radicals in Rings and Bicategories

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