Show that Q is injective if and only if, whenever $$0\to A\stackrel{f}{\to} B\stackrel{g}{\to} C\to 0$$ is exact, then $$0\to \mathrm{Hom}_R(C,Q)\stackrel{g^*}{\to} \mathrm{Hom}_R(B,Q)\stackrel{f^*}{\to} \mathrm{Hom}_R(A,Q)\to 0$$ is exact.
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