**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

**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.

(

**5243**views)

**Lectures on the Algebraic Theory of Fields**

by

**K.G. Ramanathan**-

**Tata Institute of Fundamental Research**

These lecture notes on Field theory are aimed at providing the beginner with an introduction to algebraic extensions, algebraic function fields, formally real fields and valuated fields. We assume a familiarity with group theory and vector spaces.

(

**6023**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 ...

(

**4770**views)

**Galois Theory**

by

**Miles Reid**-

**University of Warwick**

The author discusses the problem of solutions of polynomial equations both in explicit terms and in terms of abstract algebraic structures. The course demonstrates the tools of abstract algebra as applied to a meaningful problem.

(

**10169**views)