\begin{definition}[Definition:Ideal of Ring/Proper Ideal]
Let $\struct {R, +, \circ}$ be a ring.
A '''proper ideal''' $J$ of $\struct {R, +, \circ}$ is an ideal of $R$ such that $J$ is a proper subset of $R$.
That is, such that $J \subseteq R$ and $J \ne R$.
\end{definition}