Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
MathSciNet review: 614871
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16A36

Retrieve articles in all journals with MSC: 16A36

Additional Information

Article copyright: © Copyright 1981 American Mathematical Society

American Mathematical Society