## Tag `01DA`

Chapter 15: More on Algebra > Section 15.51: Injective modules

Lemma 15.51.6. Let $R$ be a ring. The functor $M \mapsto M^\vee$ is exact.

Proof.This because $\mathbf{Q}/\mathbf{Z}$ is an injective abelian group by Lemma 15.50.1. $\square$

The code snippet corresponding to this tag is a part of the file `more-algebra.tex` and is located in lines 11884–11888 (see updates for more information).

```
\begin{lemma}
\label{lemma-vee-exact}
Let $R$ be a ring.
The functor $M \mapsto M^\vee$ is exact.
\end{lemma}
\begin{proof}
This because $\mathbf{Q}/\mathbf{Z}$
is an injective abelian group by Lemma \ref{lemma-injective-abelian}.
\end{proof}
```

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