  We study the relations between partial and global group cohomology with
values in a commutative unital ring $\mathcal{A}$. In particular, for a unital
partial action of a group $G$ on $\mathcal{A}$, such that $\mathcal{A}$ is a
direct product of commutative indecomposable rings, we show that any partial
$n$-cocycle of $G$ with values in $\mathcal{A}$ is globalizable.
