The fundamental theorem of finite fields: a proof from first principles
History and Overview
2021-08-23 v2 Commutative Algebra
Number Theory
Abstract
A mathematics student's first introduction to the fundamental theorem of finite fields (FTFF) often occurs in an advanced abstract algebra course and invokes the power of Galois theory to prove it. Yet the combinatorial and algebraic coding theory applications of finite fields can show up early on for students in STEM. To make the FTFF more accessible to students lacking exposure to Galois theory, we provide a proof from algebraic "first principles."
Keywords
Cite
@article{arxiv.2010.09124,
title = {The fundamental theorem of finite fields: a proof from first principles},
author = {Anastasia Chavez and Christopher O'Neill},
journal= {arXiv preprint arXiv:2010.09124},
year = {2021}
}