  Given an arbitrary sheaf $\mathcal{E}$ of $\mathcal{A}$-modules (or
$\mathcal{A}$-module in short) on a topological space $X$, we define
\textit{annihilator sheaves} of sub-$\mathcal{A}$-modules of $\mathcal{E}$ in a
way similar to the classical case, and obtain thereafter the analog of the
\textit{main theorem}, regarding classical annihilators in module theory, see
Curtis[\cite{curtis}, pp. 240-242]. The familiar classical properties,
satisfied by annihilator sheaves, allow us to set clearly the
\textit{sheaf-theoretic version} of \textit{symplectic reduction}, which is the
main goal in this paper.
