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
Geometry of the Quinticby 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 ...
(12580 views)
Notes on Galois Theoryby 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.
(10778 views)
Lectures on the Algebraic Theory of Fieldsby 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.
(12198 views)
Fields and Galois Theoryby J. S. Milne
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; The fundamental theorem of Galois theory; etc.
(13996 views)