Galois theory
โ Scribed by Harold M. Edwards
- Book ID
- 127421091
- Publisher
- Springer
- Year
- 1997
- Tongue
- English
- Weight
- 2 MB
- Series
- Graduate Texts in Mathematics
- Category
- Library
- ISBN
- 038790980X
No coin nor oath required. For personal study only.
โฆ Synopsis
This book is an introduction to Galois theory along the lines of Galois' "Memoir on the Conditions for Solvability of Equations by Radicals". Some antecedents of Galois theory in the works of Gauss, Lagrange, Vandemonde, Newton, and even the ancient Babylonians, are explained in order to put Galois' main ideas in their historical setting. The modern formulation of the theory is also explained. The book contains many exercises - with answers - and an English translation of Galois' memoir.
๐ SIMILAR VOLUMES
Classical Galois theory is a subject generally acknowledged to be one of the most central and beautiful areas in pure mathematics. This text develops the subject systematically and from the beginning, requiring of the reader only basic facts about polynomials and a good knowledge of linear algebra.
Clearly presented elements of one of the most penetrating concepts in modern mathematics include discussions of fields, vector spaces,homogeneous linear equations, extension fields, polynomials,algebraic elements, as well as sections on solvable groups, permutation groups, solution of equations by r
Classical Galois theory is a subject generally acknowledged to be one of the most central and beautiful areas in pure mathematics. This text develops the subject systematically and from the beginning, requiring of the reader only basic facts about polynomials and a good knowledge of linear algebra.
The book discusses classical Galois theory in considerable generality, treating fields of characteristic zero and of positive characteristic with consideration of both separable and inseparable extensions, but with a particular emphasis on algebraic extensions of the field of rational numbers. While
Starting from the classical finite-dimensional Galois theory of fields, this book develops Galois theory in a much more general context. The authors first formalize the categorical context in which a general Galois theorem holds, and then give applications to Galois theory for commutative rings, cen