Galois theory and its algebraic background /
"Galois theory, the theory of polynomial equations and their solutions, is one of the most fascinating and beautiful subjects in pure mathematics. Using group theory and field theory, it provides a complete answer to the problem of the solubility of polynomial equations by radicals: that is, de...
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| Format: | Book |
| Language: | English |
| Published: |
Cambridge, United Kingdom :
Cambridge University Press,
2022
Cambridge, United Kingdom ; New York, NY : 2022 |
| Edition: | Second edition |
| Subjects: |
Table of Contents:
- Groups
- Integral domains
- Vector spaces and determinants
- Field extensions
- Ruler and compass constructions
- Splitting fields
- Normal extensions
- Separability
- The fundamental theorem of Galois theory
- The discriminant
- Cyclotomic polynomials and cyclic extensions
- Solution by radicals
- Regular polygons
- Polynomials of low degree
- Finite fields
- Quintic polynomials
- Further theory
- The algebraic closure of a field
- Transcendental elements and algebraic independence
- Generic and symmetric polynomials