Algebra

2205 Submissions

[3] viXra:2205.0029 [pdf] submitted on 2022-05-05 11:39:02

On Class Field Theory from a Group Theoretical Viewpoint

Authors: Lucian M Ionescu
Comments: 4 Pages.

The main goal of Class Field Theory, of characterizing abelian field extensions in terms of the arithmetic of the rationals, is achieved via the correspondence between Arithmetic Galois Theory and classical (algebraic) Galois Theory, as formulated in its traditional form by Artin. The analysis of field extensions, primarily of the way rational primes decompose in field extensions, is proposed, in terms of an invariant of the Galois group encoding its structure. Prospects of the non-abelian case are given in terms of Grothendieck's Anabelian Theory.
Category: Algebra

[2] viXra:2205.0021 [pdf] submitted on 2022-05-04 15:20:59

On Finite Groups and Galois Theory

Authors: Lucian M Ionescu
Comments: 5 Pages. Preliminary version

We comment on Artin's reformulation of Galois Theory incorporating MacLane's non-abelian extensions theory, and Eilenberg's Category Theory ideology.
Category: Algebra

[1] viXra:2205.0020 [pdf] submitted on 2022-05-04 15:27:41

Arithmetic Galois Theory (Part II)

Authors: Lucian M Ionescu
Comments: 20 Pages. Beamer (LaTex) presentation

A brief historic introduction to Galois Theory is followed by "Arithmetic Galois Theory", which applies the concepts of Galois objects to the category Z of cyclic groups.
Category: Algebra