On ksk-Galois theory for fields

Fields and Galois Theory

These notes give a concise exposition of the theory of fields, including the Galois theory of finite and infinite extensions and the theory of transcendental extensions. They are an expansion of those handed out during a course taught to first-year graduate students. v2.01 (August 21, 1996). First version on the web. v2.02 (May 27, 1998). Fixed about 40 minor errors; 57 pages. v3.00 (April 3, 2...

Galois Theory, Splitting Fields, and Computer Algebra

We provide some algorithms for dynamically obtaining both a possible representation of the splitting field and the Galois group of a given separable polynomial from its universal decomposition algebra. c © 2006 Elsevier Ltd. All rights reserved.

HIGHER DERrVATION GALOIS THEORY OF FIELDS

A Galois correspondence for finitely generated field extensions k/h is presented in the case characteristic h = p ^ 0. A field extension k/h is Galois if it is modular and h is separably algebraically closed in k. Galois groups are the direct limit of groups of higher derivations having rank a power of p. Galois groups are characterized in terms of abelian iterative generating sets in a manner ...

HIGHER DERrVATION GALOIS THEORY OF FIELDS

A Galois correspondence for finitely generated field extensions k/h is presented in the case characteristic h = p ^ 0. A field extension k/h is Galois if it is modular and h is separably algebraically closed in k. Galois groups are the direct limit of groups of higher derivations having rank a power of p. Galois groups are characterized in terms of abelian iterative generating sets in a manner ...

Galois deformation theory for norm fields and its arithmetic applications