\begin{definition}[Definition:Annihilator on Algebraic Dual]
Let $R$ be a commutative ring with unity.
Let $G$ be a module over $R$.
Let $G^*$ be the algebraic dual of $G$.
Let $M$ be a submodule of $G$.
The '''annihilator of $M$''' is denoted and defined as:
:$M^\circ := \set {t \in G^*: \forall x \in M: \map t x = 0}$
\end{definition}