Rings and Polynomials

Joseph Mellor
14 min readMay 16, 2022

Groups may allow for solvable equations, but we need more structure to even talk about polynomials. We call these structures rings.

This article is part 3 in the How to Discover Finite Fields While Bored in Class series. The image represents a finite commutative ring with five elements.

In the previous article, we established groups as the simplest algebraic structures with solvable equations and we showed that the five color group was isomorphic to the finite Abelian group of order five.

Joseph Mellor

BS in Physics, Math, and CS with a minor in High-Performance Computing. You can find all my articles at https://josephmellor.xyz/articles/.