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Some degeneracy and pathology in non-associative radical theory II

Published online by Cambridge University Press:  17 April 2009

B. J. Gardner
B. J. Gardner
Affiliation:
Department of Mathematics, University of Tasmania, GPO Box 252C, Hobart, Tasmania 7001, Australia.
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Abstract

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It is shown that in the universal classes of

(i) all commutative algebras,

(ii) all anti-commutative algebras and

(iii) all algebras satisfying x2 = 0 (over any commutative, associative, unital ring)

the only radical classes with hereditary semi-simple classes are those for which membership is determined by additive structure. Some examples of non-hereditary semi-simple classes in the class of all power-associative algebras are also presented.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 23 , Issue 3 , June 1981 , pp. 423 - 428
Copyright
Copyright © Australian Mathematical Society 1981

References

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