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Proceedings of the American Mathematical Society

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

 

 

Exactness of the double dual


Authors: R. R. Colby and K. R. Fuller
Journal: Proc. Amer. Math. Soc. 82 (1981), 521-526
MSC: Primary 16A36
DOI: https://doi.org/10.1090/S0002-9939-1981-0614871-5
MathSciNet review: 614871
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Abstract: Let $ R$ be an artinian ring. The double $ R$-dual ( )** preserves monomorphisms, is left exact, or is right exact if and only if $ R$ is QF-$ 3$, has dominant dimension at least 2, or is QF, respectively. Furthermore, both double dual functors preserve epimorphisms of finitely generated (left and right) modules if and only if both dual functors ( )* are exact on short exact sequences of finitely generated torsionless modules, and these conditions are equivalent to finitely generated torsionless modules being reflexive.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0614871-5
Article copyright: © Copyright 1981 American Mathematical Society