\begin{definition}[Definition:Prime Ideal of Ring/Commutative and Unitary Ring/Definition 1]
Let $\struct {R, +, \circ}$ be a commutative and unitary ring.
A '''prime ideal''' of $R$ is a proper ideal $P$ such that:
:$\forall a, b \in R : a \circ b \in P \implies a \in P$ or $b \in P$
\end{definition}