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A course in Galois theory

Author: D J H Garling
Publisher: Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1986.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

This textbook, based on lectures given over a period of years at Cambridge, is a detailed and thorough introduction to Galois theory.

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: D J H Garling
ISBN: 0521320771 9780521320771 0521312493 9780521312493
OCLC Number: 13332795
Notes: Includes index.
Description: viii, 167 pages : illustrations ; 24 cm
Contents: Preface; Part I. Algebraic Preliminaries: 1. Groups, fields and vector spaces; 2. The axiom of choice, and Zorn's lemma; 3. Rings; Part II. The Theory of Fields, and Galois Theory: 4. Field extensions; 5. Tests for irreducibility; 6. Ruler-and-compass constructions; 7. Splitting fields; 8. The algebraic closure of a field; 9. Normal extensions; 10. Separability; 11. Automorphisms and fixed fields; 12. Finite fields; 13. The theorem of the primative element; 14. Cubics and quartics; 15. Roots of unity; 16. Cyclic extensions; 17. Solution by radicals; 18. Transcendental elements and algebraic independence; 19. Some further topics; 20. The calculation of Galois groups; Index.
Other Titles: Galois theory.
Responsibility: D.J.H. Garling.
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"This is a marvellous little book. It is characterized by good mathematical taste, plain and elegant language, and an earthy but precise style." Carl Riehm, Mathematical Reviews

 
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