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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Decomposition theories for abelian categories

Authors: Joe W. Fisher and Harvey Wolff
Journal: Trans. Amer. Math. Soc. 182 (1973), 61-69
MSC: Primary 18E99
MathSciNet review: 0327870
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Abstract: Both the classical approach to decomposition theories and Fisher's technique of constructing decomposition theories from radical functions are extended to and exploited in the context of abelian categories. These two different approaches to decomposition theories for abelian categories intertwine in one theorem from which flows necessary and sufficient conditions for the existence of the tertiary, primary, and Bourbaki's $ \mathcal{P}$-primary decomposition theories.

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Keywords: Decomposition theories, abelian categories, radical functions
Article copyright: © Copyright 1973 American Mathematical Society