\begin{align*}
0 \longrightarrow P' \xrightarrow{i} P \xrightarrow{p} P'' \longrightarrow 0
\end{align*}
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be a short exact sequence of left $R$-modules. If $P''$ is projective as a left $R$-module, then the sequence splits: there exists an $R$-linear homomorphism $s:P''\to P$ such that $p\circ s=\operatorname{id}_{P''}$. Consequently,
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\begin{align*}
P \cong P' \oplus P''
\end{align*}
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as left $R$-modules. In particular, if $P'$, $P$, and $P''$ are finitely generated projective left $R$-modules, then $P\cong P'\oplus P''$.