\begin{definition}[Definition:Prime Ideal of Ring/Commutative and Unitary Ring/Definition 3]
Let $\struct {R, +, \circ}$ be a commutative and unitary ring.
A '''prime ideal''' of $R$ is a proper ideal $P$ of $R$ such that:
:the complement $R \setminus P$ of $P$ in $R$ is closed under the ring product $\circ$.
\end{definition}