A simple proof of the fundamental theorem of Galois theory

Martin Brandenburg

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arXiv · 2211.07508

A simple proof of the fundamental theorem of Galois theory

Martin Brandenburg

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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.

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Martin Brandenburg. 2022-11-14. A simple proof of the fundamental theorem of Galois theory. https://arxiv.org/abs/2211.07508

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