From $Hom(A,X)\cong Hom(B,X)$ to $A\cong B$
Abstract
Let $A$ and $B$ be two $R$-modules. We examine conditions under
which $\Hom(A,X)\cong \Hom(B,X)$, implies that $A\cong B$, where
$X$ belongs to an appropriate class of $R$-modules. Different
perspectives of the question are studied. In the case of
abelian groups ($\zz$-modules), this investigation gives a partial
answer to an old problem of L. Fuchs.
which $\Hom(A,X)\cong \Hom(B,X)$, implies that $A\cong B$, where
$X$ belongs to an appropriate class of $R$-modules. Different
perspectives of the question are studied. In the case of
abelian groups ($\zz$-modules), this investigation gives a partial
answer to an old problem of L. Fuchs.
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