Let $A$ be a local ring and $\mathcal m$ the maximal ideal, considered as an $A$-module.
Is then every $A$-module-homomorphism $\mathcal m \rightarrow A/\mathcal m$ equal to zero?
Remark: I pose this question because I read that
$Hom_A(A/\mathcal m, A/\mathcal m)$ is $A/\mathcal m$.