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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On representable linearly compact modules
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by Nguyen Tu Cuong and Le Thanh Nhan PDF
Proc. Amer. Math. Soc. 130 (2002), 1927-1936 Request permission


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:
  • Le Thanh Nhan
  • Affiliation: Institute of Mathematics, P.O. Box 631, Boho, 10.000 Hanoi, Vietnam
  • 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
  • © Copyright 2001 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 130 (2002), 1927-1936
  • MSC (1991): Primary 13C05; Secondary 13J99
  • DOI:
  • MathSciNet review: 1896024