\begin{definition}[Definition:Quotient Module]
Let $M$ be an $R$-module and $M^\ast$ be the underlying group.
Let $N$ be a submodule of $M$ and $N^\ast$ be the underlying subgroup.
Let $a + N$ denote the coset of the quotient group $M^\ast / N^\ast$.
Define the $R$-action on $M^\ast / N^\ast$ as:
:$\forall r \in R, \forall a \in M / N: r \left({a + N^\ast}\right) := r a + N^\ast$
Then $(M^\ast / N^\ast,\circ)$ is a '''quotient $R$-module'''.
\end{definition}