  Let $\Gamma$ be a graph, $A$ an abelian group, $\mathcal{D}$ a given
orientation of $\Gamma$ and $R$ a unital subring of the endomorphism ring of
$A$. It is shown that the set of all maps $\varphi$ from $E(\Gamma)$ to $A$
such that $(\mathcal{D},\varphi)$ is an $A$-flow forms a left $R$-module. Let
$\Gamma$ be a union of two subgraphs $\Gamma_{1}$ and $\Gamma_{2}$, and $p^n$ a
prime power. It is proved that $\Gamma$ admits a nowhere-zero $p^n$-flow if
$\Gamma_{1}$ and $\Gamma_{2}$ have at most $p^n-2$ common edges and both have
nowhere-zero $p^n$-flows. More important, it is proved that $\Gamma$ admits a
nowhere-zero $4$-flow if $\Gamma_{1}$ and $\Gamma_{2}$ both have nowhere-zero
$4$-flows and their common edges induce a connected subgraph of $\Gamma$ of
size at most $3$. This covers a result of Catlin that a graph admits a
nowhere-zero $4$-flow if it is a union of a $4$-cycle and a subgraph admiting a
nowhere-zero $4$-flow.
