Generic Polynomials: Constructive Aspects of the Inverse Galois Problem
by C. U. Jensen, A. Ledet, N. Yui
Publisher: Cambridge University Press 2002
Number of pages: 268
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.
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by Christopher Cooper - Macquarie University
This text follows the usual path through to Galois groups, but just for subfields of the complex numbers. It takes as its goal the insolubility of polynomials by radicals. There is a chapter that gives a proof of the Fundamental Theorem of Algebra.
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.
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.
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.