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Some degeneracy and pathology in non-associative radical theory II
Published online by Cambridge University Press: 17 April 2009
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.
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- Copyright © Australian Mathematical Society 1981
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