Symplectic Reduction of Sheaves of $\mathcal{A}$-modules

Given an arbitrary sheaf $\mathcal{E}$ of $\mathcal{A}$-modules (or $\mathcal{A}$-module in short) on a topological space $X$, we define $\mathit{\text{annihilator}}\mathit{\text{sheaves}}$ of sub-$\mathcal{A}$-modules of $\mathcal{E}$ in a way similar to the classical case, and obtain thereafter the analog of the $\mathit{\text{main}}\mathit{\text{theorem}}$, 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 $\mathit{\text{sheaf-theoretic}}\mathit{\text{version}}$ of $\mathit{\text{symplectic}}\mathit{\text{reduction}}$, which is the main goal in this paper.