= Character module
{title2=$M^*=\operatorname{Hom}_{\mathbb Z}(M,\mathbb Q/\mathbb Z)$}
= Character dual
{synonym}
For a <module> $M$ over a commutative <ring> $A$, its character module is the additive-group dual into $D=\mathbb Q/\mathbb Z$, with action $(a\phi)(m)=\phi(am)$. The group $D$ is an <injective cogenerator of abelian groups>. The natural adjunction $\operatorname{Hom}_A(N,M^*)\cong\operatorname{Hom}_{\mathbb Z}(N\otimes_AM,D)$ sends $h$ to the balanced pairing $(n,m)\mapsto h(n)(m)$.
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