Math 361, Spring 2022, Assignment 12

Carefully define the following terms, and give one example and one non-example of each:

1. Principal ideal domain (a.k.a. PID).

Carefully state the following theorems (you do not need to prove them):

1. List of units of $F[x]$.
2. Theorem relating maximal ideals to irreducible elements (in PIDs).
3. Criterion for $F[x]/\left\langle m\right\rangle$ to be a field.

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