Transfinite Galois Theory

Alec Rhea

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arXiv · 1712.00662

Transfinite Galois Theory

Alec Rhea

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Abstract

In this paper I generalize the notion of a polynomial over an ordered field to that of a naked polynomial over a non-Archimedean ordered field, subsequently showing that the notion of a naked polynomial ring forms an Euclidean domain. This canonically generalizes the methods of Galois theory of fields and polynomial rings to a transfinite Galois theory of non-Archimedean ordered fields and naked polynomial rings, lifting the processes of splitting and algebraic closure to non-Archimedean ordered fields.

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Alec Rhea. 2017-12-02. Transfinite Galois Theory. https://arxiv.org/abs/1712.00662

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