  We study partial homology and cohomology from ring theoretic point of view
via the partial group algebra $\mathbb{K}_{par}G$. In particular, we link the
partial homology and cohomology of a group $G$ with coefficients in an
irreducible (resp. indecomposable) $\mathbb{K}_{par}G$-module with the ordinary
homology and cohomology groups of $G$ with in general non-trivial coefficients.
Furthermore, we compare the standard cohomological dimension $cd_{ \
\mathbb{K}}(G)$ (over a field $\mathbb{K}$) with the partial cohomological
dimension $cd_{ \ \mathbb{K}}^{par}(G)$ (over $\mathbb{K}$) and show that $cd_{
\ \mathbb{K}}^{par}(G) \geq cd_{ \ \mathbb{K}}(G)$ and that there is equality
for $G = \mathbb{Z}$.
