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Galois theory / Joseph Rotman.

By: Material type: TextLanguage: English Series: UniversitextPublication details: New York : Springer New York, 1998.Edition: Second editionDescription: 1 online resource (169 pages) : illustrationsISBN:
  • 9781461206170 (ebook)
Subject(s): Additional physical formats: Print version:: Galois theory.DDC classification:
  • 512.3 21 ROT
Online resources:
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.
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. 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.
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Cover image Item type Current library Home library Collection Shelving location Call number Materials specified Vol info URL Copy number Status Notes Date due Barcode Item holds Item hold queue priority Course reserves
General Books CUTN Central Library Sciences Non-fiction 512.3 ROT (Browse shelf(Opens below)) Available 49586

Electronic reproduction. Ann Arbor, MI : ProQuest, 2016. Available via World Wide Web. Access may be limited to ProQuest affiliated libraries.

Includes bibliographical references and index.

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.

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The first edition aimed to give a geodesic path to the Fundamental Theorem of Galois Theory, and I still think its brevity is valuable. 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.

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