Ideal of Ring of Polynomials over Field has Unique Monic Polynomial forming Principal Ideal
Let $F$ be a field.
Let $F \sqbrk X$ be the ring of polynomials in $X$ over $F$.
- $J = \ideal f$
where $\ideal f$ is the principal ideal generated by $f$ in $F \sqbrk X$.
Let $f_1$ and $f_2$ be generators of $J$.
Then $f_1$ and $f_2$ are unit multiples of each other.