Foundations of Galois Theory: M. M. Postnikov: 9780486435183: Book: Technology: eCampus.com

Written by a prominent mathematician, this text offers advanced undergraduate and graduate students a virtually self-contained treatment of the basics of Galois theory. This two-part approach begins with the elements of Galois theory, focusing on related concepts from field theory, and a consideration of relevant facts from group theory leads to a survey of Galois theory. The second part explores the solution of equations by radicals, returning to the general theory of groups for relevant facts, examining equations solvable by radicals and their construction, and concluding with the unsolvability by radicals of the general equation of degree n > 5. 1962 ed.

The first part explores�Galois theory, focusing on related concepts from field theory. The second part discusses the solution of equations by radicals, returning to the general theory of groups for relevant facts, examining equations solvable by radicals and their construction, and concludes with the unsolvability by radicals of the general equation of degree n > 5. 1962 edition.

Foreword

vii

Preface

viii

I. THE ELEMENTS OF GALOIS THEORY

1. THE ELEMENTS OF FIELD THEORY

(15)

1. Preliminary remarks

(1)

2. Some important types of extensions

(2)

3. The minimal polynomial. The structure of simple algebraic extensions

(2)

4. The algebraic nature of finite extensions

(1)

5. The structure of composite algebraic extensions

(2)

6. Composite finite extensions

(3)

7. The theorem that a composite algebraic extension is simple

(2)

8. The field of algebraic numbers

(1)

9. The composition of fields

(2)

2. NECESSARY FACTS FROM THE THEORY OF GROUPS

(9)

1. The definition of a group

(2)

2. Subgroups, normal divisors and factor groups

(3)

3. Homomorphic mappings

(4)

3. GALOIS THEORY

(20)

1. Normal extensions

(3)

2. Automorphisms of fields. The Galois group

(3)

3. The order of the Galois group

(4)

4. The Galois correspondence

(3)

5. A theorem about conjugate elements

(1)

6. The Galois group of a normal subfield

(2)

7. The Galois group of the composition of two fields

(4)

II. THE SOLUTION OF EQUATIONS BY RADICALS

1. ADDITIONAL FACTS FROM THE GENERAL THEORY OF GROUPS

(13)

1. A generalization of the homomorphism theorem

(1)

2. Normal series

(3)

3. Cyclic groups

(3)

4. Solvable and Abelian groups

(6)

2. EQUATIONS SOLVABLE BY RADICALS

(15)

1. Simple radical extensions

(2)

2. Cyclic extensions

(5)

3. Radical extensions

(3)

4. Normal fields with solvable Galois group

(3)

5. Equations solvable by radicals

(2)

3. THE CONSTRUCTION OF EQUATIONS SOLVABLE BY RADICALS

(19)

1. The Galois group of an equation as a group of permutations

(2)

2. The factorization of permutations into the product of cycles

(4)

3. Even permutations. The alternating group

(2)

4. The structure of the alternating and symmetric groups

(4)

5. An example of an equation with Galois group the symmetric group

(4)

6. A discussion of the results obtained

(3)

4. THE UNSOLVABILITY BY RADICALS OF THE GENERAL EQUATION OF DEGREE n > or equal to 5

1. The field of formal power series

(5)

2. The field of fractional power series

(4)

3. The Galois group of the general equation of degree n

101

(4)

4. The solution of equations of low degree

105


	Buy Textbooks Sell Textbooks College Apparel Shop by School Virtual Bookstores	Order Status Shipping Rates Return Policy Marketplace Info F.A.S.T.	Contact Us Privacy Policy Legal Notices Site Security Employment	Help Desk eCampus Blog Affiliate Program Bulk Orders College Marketing

Need Help? eService@ecampus.com Copyright© 1999-2008
.