论文标题
有限领域的基本定理：第一原则的证明
The fundamental theorem of finite fields: a proof from first principles
论文作者
论文摘要
数学学生对有限领域基本定理（FTFF）的首次介绍通常发生在先进的抽象代数课程中，并援引Galois理论的力量来证明这一点。然而，有限领域的组合和代数编码理论的应用可能会在STEM的学生早期出现。为了使FTFF更容易被缺乏加洛伊斯理论的学生提供，我们提供了代数“第一原则”的证明。
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."
