UID:
edocfu_9959235947802883
Format:
1 online resource (li, 294 pages) :
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digital, PDF file(s).
ISBN:
1-139-88164-7
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1-107-26676-9
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1-107-26319-0
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1-107-26983-0
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1-107-34074-8
Series Statement:
Encyclopedia of mathematics and its applications. Section, Algebra ;
Content:
Originally published in 1984, the principal objective of this book is to make the general theory of field extensions accessible to any reader with a modest background in groups, rings and vector spaces. Galois theory is generally regarded as one of the central and most beautiful parts of algebra and its creation marked the culmination of investigations by generations of mathematicians on one of the oldest problems in algebra, the solvability of polynomial equations by radicals.
Note:
Imprint and ISBN from label on t.p. verso. Imprint on t.p.: Reading, Mass. : Addison-Wesley, Advanced Book Program, 1984.
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Publication taken over by Cambridge University Press in 1984.
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Includes index.
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Cover; Half Title; Series Page; Title; Copyright; Dedication; Contents; Editor's Statement; Foreword; Preface; Historical Introduction; Prerequisites; Notation; NOTATION PERTAINING TO THE THEORY OF FIELD EXTENSIONS AND GALOIS THEORY; Chapter 1 Preliminaries on Fields and Polynomials; 1.1. FIELDS OF FRACTIONS; PROBLEMS; 1.2. THE CHARACTERISTIC; 1.2.1. Examples; PROBLEMS; 1.3. PERFECT FIELDS AND PRIME FIELDS; PROBLEMS; 1.4. FIELD EXTENSIONS; 1.4.1. Examples; PROBLEMS; 1.5. FACTORIZATION OF POLYNOMIALS; 1.5.10. Examples; PROBLEMS; 1.6. SPLITTING OF POLYNOMIALS; 1.6.1. Examples; 1.6.2. Examples
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1.6.6. ExamplesPROBLEMS; 1.7. SEPARABLE POLYNOMIALS; 1.7.4. Examples; PROBLEMS; NOTES; Chapter 2 Algebraic Extensions; 2.1. ALGEBRAIC EXTENSIONS; 2.1.1. Examples; 2.1.7. Examples; PROBLEMS; 2.2. ALGEBRAICALLY CLOSED FIELDS; 2.2.8. Examples; PROBLEMS; 2.3. NORMAL EXTENSIONS; 2.3.1. Examples; 2.3.16. Examples; PROBLEMS; 2.4. PURELY INSEPARABLE EXTENSIONS; PROBLEMS; 2.5. SEPARABLE EXTENSIONS; PROBLEMS; NOTES; Chapter 3 Galois Theory; 3.1. SOME VECTOR SPACES OF MAPPINGS OF FIELDS; 3.1.4. Examples; PROBLEMS; 3.2. THE GENERAL GALOIS CORRESPONDENCES; 3.2.4. Examples; PROBLEMS; 3.3. GALOIS EXTENSIONS
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PROBLEMS3.4. FINITE GALOIS THEORY; PROBLEMS; 3.5. ROOTS OF UNITY; PROBLEMS; 3.6. PRIMITIVE ELEMENTS; PROBLEMS; 3.7. SEPARABLE AND INSEPARABLE DEGREES; PROBLEMS; 3.8. NORMS AND TRACES; 3.8.1. Examples; PROBLEMS; 3.9. CYCLIC EXTENSIONS; PROBLEMS; 3.10. SOLVABILITY BY RADICALS; PROBLEMS; 3.11. FINITE FIELDS; 3.11.4. Examples; PROBLEMS; 3.12. INFINITE GALOIS THEORY; PROBLEMS; NOTES; Suggestions for further reading; Chapter 4 Transcendental Extensions; 4.1. DIMENSIONAL OPERATORS; 4.1.1. Examples; 4.1.2. Examples; PROBLEMS; 4.2. TRANSCENDENCE BASES AND TRANSCENDENCE DEGREE; PROBLEMS
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4.3. SPECIALIZATIONS AND PLACES OF FIELDS4.3.1. Examples; PROBLEMS; 4.4. SEPARABLE EXTENSIONS; PROBLEMS; 4.5. DERIVATIONS OF FIELDS; 4.5.1. Examples; 4.5.5. Examples; PROBLEMS; 4.6. DERIVATIONS OF ALGEBRAIC FUNCTION FIELDS; PROBLEMS; NOTES; Suggestions for further reading; References and Selected Bibliography; Bibliography; Of historical interest; Index
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English
Additional Edition:
ISBN 0-521-17396-5
Additional Edition:
ISBN 0-521-30242-0
Language:
English
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