Abstract
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.
Publisher
Cambridge University Press (CUP)
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Cited by
2 articles.
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1. Some remarks on general radical theory and distributive near-rings;Acta Mathematica Hungarica;1992
2. Some Pathology for Radicals in Non-Associative Near-Rings;Near-Rings and Near-Fields, Proceedings of a Conference held at the University of Tübingen, F.R.G.;1987