A simple proof of the fundamental theorem of Galois theory

Abstract

We present a simple proof of the fundamental theorem of Galois theory, which establishes a correspondence between the intermediate fields of a finite Galois extension and the subgroups of its Galois group. The proof is based on the combinatorial fact that a field cannot be expressed as the union of finitely many proper subfields.

arXiv comment7 pages. v2: removed incorrect claim in Rem. 2.4 + minor adjustments