Galois Theory / by Joseph Rotman.

Format:

Book

Author/Creator:

Rotman, Joseph., Author.

Series:

Universitext, 2191-6675

Language:

English

Subjects (All):

Group theory.

Group Theory and Generalizations.

Local Subjects:

Group Theory and Generalizations.

Physical Description:

1 online resource (XIV, 176 p.)

Edition:

2nd ed. 1998.

Place of Publication:

New York, NY : Springer New York : Imprint: Springer, 1998.

Language Note:

English

Summary:

The first edition aimed to give a geodesic path to the Fundamental Theorem of Galois Theory, and I still think its brevity is valuable. Alas, the book is now a bit longer, but I feel that the changes are worthwhile. I began by rewriting almost all the text, trying to make proofs clearer, and often giving more details than before. Since many students find the road to the Fundamental Theorem an intricate one, the book now begins with a short section on symmetry groups of polygons in the plane; an analogy of polygons and their symmetry groups with polynomials and their Galois groups can serve as a guide by helping readers organize the various definitions and constructions. The exposition has been reorganized so that the discussion of solvability by radicals now appears later; this makes the proof of the Abel-Ruffini theo rem easier to digest. I have also included several theorems not in the first edition. For example, the Casus Irreducibilis is now proved, in keeping with a historical interest lurking in these pages.

Contents:

Symmetry

Rings

Domains and Fields

Homomorphisms and Ideals

Quotient Rings

Polynomial Rings over Fields

Prime Ideals and Maximal Ideals

Irreducible Polynomials

Classical Formulas

Splitting Fields

The Galois Group

Roots of Unity

Solvability by Radicals

Independence of Characters

Galois Extensions

The Fundamental Theorem of Galois Theory

Applications

Galois’s Great Theorem

Discriminants

Galois Groups of Quadratics, Cubics, and Quartics

Epilogue

Appendix A: Group Theory Dictionary

Appendix B: Group Theory Used in the Text

Appendix C: Ruler-Compass Constructions

Appendix D: Old-fashioned Galois Theory

References.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

ISBN:

1-4612-0617-0