**Fields and Galois Theory**

by J. S. Milne

2008**Number of pages**: 111

**Description**:

A concise treatment of Galois theory and the theory of fields, including transcendence degrees and infinite Galois extensions. Contents: Basic definitions and results. Splitting fields; multiple roots. The fundamental theorem of Galois theory. Computing Galois groups. Applications of Galois theory. Algebraic closures. Infinite Galois theory. Transcendental Extensions.

Download or read it online for free here:

**Download link**

(940KB, PDF)

## Similar books

**Algebraic Equations**

by

**George Ballard Mathews**-

**Cambridge University Press**

This book is intended to give an account of the theory of equations according to the ideas of Galois. This method analyzes, so far as exact algebraical processes permit, the set of roots possessed by any given numerical equation.

(

**6064**views)

**Lectures on Field Theory and Ramification Theory**

by

**Sudhir R. Ghorpade**-

**Indian Institute of Technology, Bombay**

These are notes of a series of lectures, aimed at covering the essentials of Field Theory and Ramification Theory as may be needed for local and global class field theory. Included are the two sections on cyclic extensions and abelian extensions.

(

**6067**views)

**Class Field Theory**

by

**J. S. Milne**

Class field theory describes the abelian extensions of a local or global field in terms of the arithmetic of the field itself. These notes contain an exposition of abelian class field theory using the algebraic/cohomological approach.

(

**7031**views)

**Geometry of the Quintic**

by

**Jerry Shurman**-

**Wiley-Interscience**

The text demonstrates the use of general concepts by applying theorems from various areas in the context of one problem -- solving the quintic. This book helps students to develop connections between the algebra, geometry, and analysis ...

(

**5628**views)