Prime and irreducible elements in a commutative ring
Let
- Define what it means for an element in
to be prime, and also what it means for an element to be irreducible. - Prove that if
is an integral domain, then every prime element is irreducible.
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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}