Transfinite Galois Theory
Rings and Algebras
2017-12-05 v1 Commutative Algebra
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.
Keywords
Cite
@article{arxiv.1712.00662,
title = {Transfinite Galois Theory},
author = {Alec Rhea},
journal= {arXiv preprint arXiv:1712.00662},
year = {2017}
}
Comments
9 pages