ABSTRACT
Introductory courses in modern algebra usually present groups, rings, and fields as the three most important algebraic structures. Though fields are a particular class of rings, they possess unique properties that lead to many fruitful investigations. This is why they are often viewed as their own algebraic structure. Chapter 6 studied properties of divisibility in commutative rings. Since every nonzero element in a field has a multiplicative inverse, questions concerning divisibility are not interesting: Every nonzero element is an associate to every other. Nonetheless, fields possess a rich structure.
