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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Radical and semisimple classes with specified properties


Author: W. G. Leavitt
Journal: Proc. Amer. Math. Soc. 24 (1970), 680-687
MSC: Primary 17.10
DOI: https://doi.org/10.1090/S0002-9939-1970-0252454-2
Erratum: Proc. Amer. Math. Soc. 25 (1970), 922.
MathSciNet review: 0252454
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Abstract: Conditions are given on a radical (semisimple) property to ensure the existence of a construction for the smallest radical (semisimple) class with the property, containing a given class of rings. This generalizes earlier results on smallest hereditary or strongly hereditary radical classes, and hereditary semisimple classes. In the last section certain classes of rings are shown to admit a construction for the largest radical (semisimple) class contained in the given class. This leads to theorems on largest radical (semisimple) classes dual to the already established smallest theorems.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0252454-2
Keywords: General radical classes, semisimple classes, hereditary radical, smallest class of rings with a specified property, largest class of rings with a specified property contained in a given class, lower radical construction
Article copyright: © Copyright 1970 American Mathematical Society