Polynomials with even constant term
Let
- Prove that
is an ideal. - Prove that
is not a principal ideal.
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Let $I\subseteq {\bf Z}[x]$ denote the set of all polynomials with even constant term.
\begin{enumerate}[label=\alph*)]
\item Prove that $I$ is an ideal.
\item Prove that $I$ is not a {\itshape principal} ideal.
\end{enumerate}