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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On representable linearly compact modules


Authors: Nguyen Tu Cuong and Le Thanh Nhan
Journal: Proc. Amer. Math. Soc. 130 (2002), 1927-1936
MSC (1991): Primary 13C05; Secondary 13J99
Published electronically: December 31, 2001
MathSciNet review: 1896024
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Abstract: For a flat $R-$module $F,$ we prove that $\operatorname{Hom}_{R}(F,-)$ is a functor from the category of linearly compact $R-$modules to itself and is exact. Moreover, $\operatorname{Hom}_{R}(F,M)$ is representable when $M$ is linearly compact and representable. This gives an affirmative answer to a question of L. Melkersson (1995) for linearly compact modules without the condition of finite Goldie dimension. The set of attached prime ideals of the co-localization $\operatorname{Hom}_{R}(R_{S},M)$ of a linearly compact representable $R-$module $M$ with respect to a multiplicative set $S$ in $R$ is described.


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Additional Information

Nguyen Tu Cuong
Affiliation: Institute of Mathematics, P.O. Box 631, Boho, 10.000 Hanoi, Vietnam
Email: Cuongnt@hn.vnn.vn

Le Thanh Nhan
Affiliation: Institute of Mathematics, P.O. Box 631, Boho, 10.000 Hanoi, Vietnam

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06298-0
PII: S 0002-9939(01)06298-0
Keywords: Linearly compact module, secondary representation, co-localization
Received by editor(s): September 20, 2000
Received by editor(s) in revised form: February 1, 2001
Published electronically: December 31, 2001
Additional Notes: This work was supported in part by the National Basis Research Program in Natural Science of Vietnam
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 2001 American Mathematical Society