The Uniqueness of the Field of Complex Numbers
William Wynne Willson · Mathematics Teacher Learning and Teaching PK-12 · 1969
IN A recent paper in this journal Dorman, Tollefson, and Stein1 considered under what binary operations of addition and multiplication the set S of ordered pairs of real numbers becomes a field. In particular they showed that the three following assumptions lead to infinitely many possible fields, which they classified into three types. The assumptions are these: