Classical Galois Theory with Examples
Published on 30. October 1998
Book
Hardback
248 pages
978-0-8218-1375-1 (ISBN)
Description
Galois theory is one of the most beautiful subjects in mathematics, but it is heard to appreciate this fact fully without seeing specific examples. Numerous examples are therefore included throughout the text, in the hope that they will lead to a deeper understanding and genuine appreciation of the more abstract and advanced literature on Galois theory. This book is intended for beginning graduate students who already have some background in algebra, including some elementary theory of groups, rings and fields. The expositions and proofs are intended to present Galois theory in as simple a manner as possible, sometimes at the expense of brevity. The book is for students and intends to make them take an active part in mathematics rather than merely read, nod their heads at appropriate places, skip the exercises, and continue on to the next section.
More details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
Illustrations
Illustrations
Weight
490 gr
ISBN-13
978-0-8218-1375-1 (9780821813751)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
New editions
Lisl Gaal
Classical Galois Theory with Examples
Book
04/1971
American Mathematical Society
€93.04
Article not available at the moment
Content
Prerequisites: 1.1 Group theory; 1.2 Permutations and permutation groups; 1.3 Fields; 1.4 Rings and polynomials; 1.5 Some elementary theory of equations; 1.6 Vector spaces Fields: 2.1 Degree of an algebraic extension; 2.2 Isomorphisms of fields; 2.3 Automorphisms of fields; 2.4 Fixed fields Fundamental theorem: 3.1 Splitting fields; 3.2 Normal extensions and groups of automorphisms; 3.3 Conjugate fields and elements; 3.4 Fundamental theorem Applications: 4.1 Solvability of equations; 4.2 Solvable equations have solvable groups; 4.3 General equation of degree $n$; 4.4 Roots of unity and cyclic equations; 4.5 How to solve a solvable equation; 4.6 Ruler-and-compass constructions; 4.7 Lagrange's theorem; 4.8 Resolvent of a polynomial; 4.9 Calculation of the Galois group; 4.10 Matrix solutions of equations; 4.11 Finite fields; 4.12 More applications Bibliography Index.