Prime and irreducible elements in a commutative ring

#ring_theory

Let $R$ be a commutative ring with unity.
(a) Define what it means for an element in $R$ to be prime, and also what it means for an element to be irreducible.
(b) Prove that if $R$ is an integral domain, then every prime element is irreducible.

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L A T E X

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Let $R$ be a commutative ring with unity.
\begin{enumerate}[label=\alph*)]
	\item Define what it means for an element in $R$ to be {\bfseries prime}, and also what it means for an element to be {\bfseries irreducible}.
	\item Prove that if $R$ is an integral domain, then every prime element is irreducible.
\end{enumerate}