Galois theory
著者
書誌事項
Galois theory
（Universitext）
Springer-Verlag, c1990
- : us
- : gw
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注記
Includes bibliographical references and index
内容説明・目次
- 巻冊次
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: us ISBN 9780387973050
内容説明
This text offers a clear, efficient exposition of Galois Theory with exercises and complete proofs. Topics include: Cardano's formulas; the Fundamental Theorem; Galois' Great Theorem (solvability for radicals of a polynomial is equivalent to solvability of its Galois Group); and computation of Galois group of cubics and quartics. There are appendices on group theory and on ruler-compass constructions. Developed on the basis of a second-semester graduate algebra course, following a course on group theory, this book will provide a concise introduction to Galois Theory suitable for graduate students, either as a text for a course or for study outside the classroom.
目次
Rings.- Homomorphisms and Ideals.- Quotient Rings.- Polynomial Rings over Fields.- Prime Ideals and Maximal Ideals.- Finite Fields.- Irreducible Polynomials.- Classical Formulas.- Splitting Fields.- Solvability by Radicals.- The Galois Group.- Primitive Roots of Unity.- Insolvability of the Quintic.- Independence of Characters.- Galois Extensions.- Fundamental Theorem of Galois Theory.- Applications.- Galois’s Great Theorem.- Discriminants.- Galois Groups of Quadratics, Cubics, and Quartics.- Epilogue.- Appendix 1. Group Theory Dictionary.- Appendix 2. Group Theory Used in the Text.- Appendix 3. Ruler-Compass Constructions.- Appendix 4. Old-fashioned Galois Theory.- References.
- 巻冊次
-
: gw ISBN 9783540973058
内容説明
This text offers an exposition of Galois theory with exercises and complete proofs. Topics include Cardano's formulas, the fundamental theorem, Galois' great theorem (solvability for radicals of a polynomial is equivalent to solvability of its Galois group), and computation of Galois groups of cubics and quartics. There are appendices on group theory and ruler-compass constructions. Developed on the basis of a graduate algebra course, following a course on group theory, this book will provide a concise introduction to Galois theory suitable for graduate students, either as a text for a course or for study outside the classroom.
目次
Contents: Rings.- Homomorphisms and Ideas.- Quotient Rings.- Polynomial Rings over Fields.- Prime Ideas and Maximal Ideals.- Finite Fields.- Irreducible Polynomials.- Classical Formulas.- Splitting Fields.- Solvability by Radicals.- The Galois Group.- Primitive Roots of Unity.- Insolvability of the Quintic.- Independence of Characters.- Galois Extensions.- Fundamental Theorem of Galois Theory.- Applications.- Galois' Great Theorem.- Discriminants.- Galois Group of Quadratics, Cubics, and Quartics.- Epilogue.- Appendices.- References.- Index.
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