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