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

by C. U. Jensen, A. Ledet, N. Yui

**Publisher**: Cambridge University Press 2002**ISBN/ASIN**: 0521819989**ISBN-13**: 9780521819985**Number of pages**: 268

**Description**:

This book describes a constructive approach to the Inverse Galois problem. The main theme is an exposition of a family of "generic" polynomials for certain finite groups, which give all Galois extensions having the required group as their Galois group. The existence of such generic polynomials is discussed, and where they do exist, a detailed treatment of their construction is given. The book also introduces the notion of "generic dimension" to address the problem of the smallest number of parameters required by a generic polynomial.

Download or read it online for free here:

**Download link**

(1.8MB, PDF)

## Similar books

**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.

(

**5496**views)

**Notes on Galois Theory**

by

**Mark Reeder**-

**Boston College**

From the table of contents: Basic ring theory, polynomial rings; Finite fields; Extensions of rings and fields; Computing Galois groups of polynomials; Galois groups and prime ideals; Cyclotomic extensions and abelian numbers.

(

**3070**views)

**Galois Theory: Lectures Delivered at the University of Notre Dame**

by

**Emil Artin**-

**University of Notre Dame**

The book deals with linear algebra, including fields, vector spaces, homogeneous linear equations, and determinants, extension fields, polynomials, algebraic elements, splitting fields, group characters, normal extensions, roots of unity, and more.

(

**286**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 ...

(

**4129**views)