Transfinite Galois Theory
Abstract
In this paper I generalize the notion of a polynomial over an ordered field to that of a naked polynomial over a nonArchimedean 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 nonArchimedean ordered fields and naked polynomial rings, lifting the processes of splitting and algebraic closure to nonArchimedean ordered fields.
 Publication:

arXiv eprints
 Pub Date:
 December 2017
 DOI:
 10.48550/arXiv.1712.00662
 arXiv:
 arXiv:1712.00662
 Bibcode:
 2017arXiv171200662R
 Keywords:

 Mathematics  Rings and Algebras;
 Mathematics  Commutative Algebra;
 12XX
 EPrint:
 9 pages