Artin–Zorn theorem

In mathematics, the Artin–Zorn theorem is an important idea named after two mathematicians, Emil Artin and Max Zorn. This theorem tells us that a small, special kind of number system, called a finite alternative division ring, is actually a more common number system known as a finite field.

The theorem was first shared in 1930 by Zorn, but he gave credit to Artin for the idea. It builds on another result called Wedderburn's little theorem. One interesting result from the Artin–Zorn theorem is that a special kind of geometric space, called a finite Moufang plane, is actually a basic projective plane created using a finite field. This theorem helps mathematicians understand number systems and their connections to geometry.