Direct products and the contravariant hom-functor

Details Direct products and the contravariant hom-functor Direct products and the contravariant hom-functor

2011-05-23

arxiv.org/abs/1105.4399v1

Mathematics

Rings and Algebras

Scientific paper

10.1112/blms/bdr083

We prove in ZFC that if $G$ is a (right) $R$-module such that the groups
$\Hom_R(\prod_{i\in I}G_i,G)$ and $\prod_{i\in I}\Hom_R(G_i,G)$ are naturally
isomorphic for all families of $R$-modules $(G_i)_{i\in I}$ then G=0. The
result is valid even we restrict to families such that $G_i\cong G$ for all
$i\in I$.

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