**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

**Generic Polynomials: Constructive Aspects of the Inverse Galois Problem**

by

**C. U. Jensen, A. Ledet, N. Yui**-

**Cambridge University Press**

A clearly written book, which uses exclusively algebraic language (and no cohomology), and which will be useful for every algebraist or number theorist. It is easily accessible and suitable also for first-year graduate students.

(

**10220**views)

**The Elements of the Theory of Algebraic Numbers**

by

**Legh Wilber Reid**-

**The Macmillan company**

It has been my endeavor in this book to lead by easy stages a reader, entirely unacquainted with the subject, to an appreciation of some of the fundamental conceptions in the general theory of algebraic numbers. Many numerical examples are given.

(

**4815**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.

(

**5383**views)

**Lectures On Galois Cohomology of Classical Groups**

by

**M. Kneser**-

**Tata Institute of Fundamental Research**

The main result is the Hasse principle for the one-dimensional Galois cohomology of simply connected classical groups over number fields. For most groups, this result is closely related to other types of Hasse principle.

(

**4935**views)