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 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- December 2017
- DOI:
- 10.48550/arXiv.1712.00662
- arXiv:
- arXiv:1712.00662
- Bibcode:
- 2017arXiv171200662R
- Keywords:
-
- Mathematics - Rings and Algebras;
- Mathematics - Commutative Algebra;
- 12-XX
- E-Print:
- 9 pages