On page 222 of Nicholson: Introduction to Abstract Algebra in his section of Factor Rings of Polynomials Over a Field we find Theorem 1 stated as follows: (see attached)

Let F be a field and let $\displaystyle A \ne 0 $ be an ideal of F[x]. Then a uniquely determined monic polynomial h exists exists in F[x] such that A = (h).Theorem 1.

The beginning of the proof reads as follows:

Because $\displaystyle A \ne 0 $, it contains non-zero polynomials and hence contains monic polynomials (being an ideal) ... ... etc. etc.Proof:

BUT! why must A contain monic polynomials??

Help with this matter would be appreciated!

Peter