Polynomial Ideal Fx is a Principle Ideal Domain

Theorem

• Let $M$ be a non-zero Polynomial Ideal in $\mathbb{F}[x]$
• Then there exists a unique Monic Polynomial $d\in \mathbb{F}[x]$ such that $M$ is the Principle Polynomial Ideal generated by $d$.

This monic found by finding the Greatest Common Divisor of Polynomials in the set $M$