Galois theory /
Rotman, Joseph J., 1934-
Galois theory / Joseph Rotman. - Second edition. - New York : Springer New York, 1998. - 1 online resource (169 pages) : illustrations. - Universitext. . - Universitext. .
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.
Access restricted to subscribing institutions.
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.
9781461206170 (ebook)
Galois theory.
512.3 / ROT
Galois theory / Joseph Rotman. - Second edition. - New York : Springer New York, 1998. - 1 online resource (169 pages) : illustrations. - Universitext. . - Universitext. .
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.
Access restricted to subscribing institutions.
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.
9781461206170 (ebook)
Galois theory.
512.3 / ROT