On representable linearly compact modules

Cuong, Nguyen; Nhan, Le Thanh

doi:10.1090/S0002-9939-01-06298-0

On representable linearly compact modules
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by Nguyen Tu Cuong and Le Thanh Nhan

Proc. Amer. Math. Soc. 130 (2002), 1927-1936

DOI: https://doi.org/10.1090/S0002-9939-01-06298-0

Published electronically: December 31, 2001

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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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