\begin{definition}[Definition:Prime Ideal of Ring/Commutative and Unitary Ring/Definition 2]
Let $\struct {R, +, \circ}$ be a commutative and unitary ring.
A '''prime ideal''' of $R$ is a proper ideal $P$ of $R$ such that:
:$I \circ J \subseteq P \implies I \subseteq P \text { or } J \subseteq P$
for all ideals $I$ and $J$ of $R$.
\end{definition}