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- catalog abstract "This text offers a clear, efficient exposition of Galois Theory with complete proofs and exercises. Topics include: cubic and quartic formulas; Fundamental Theory of Galois Theory; insolvability of the quintic; Galois's Great Theorem (solvability by 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, ruler-compass constructions, and the early history of Galois Theory. This book provides a concise introduction to Galois Theory suitable for first-year graduate students, either as a text for a course or for study outside the classroom. This new edition has been completely rewritten. Proofs are now clearer because more details are given and because the exposition has been reorganized (for example, the discussion of solvability by radicals now appears later in the book). The book now begins with a short section on symmetry groups of polygons in the plane, for there is an analogy between symmetry groups of polygons and Gaulois groups of polynomials. This analogy can serve as a guide to help readers organize the various field theoretic definitions and constructions. Several new theorems habe also been included; for example, the Casus Irreducibilis.".
- catalog contributor b10990315.
- catalog created "c1998.".
- catalog date "1998".
- catalog date "c1998.".
- catalog dateCopyrighted "c1998.".
- catalog description "Includes bibliographical references (p.151-152) and index.".
- catalog description "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. Index.".
- catalog description "This text offers a clear, efficient exposition of Galois Theory with complete proofs and exercises. Topics include: cubic and quartic formulas; Fundamental Theory of Galois Theory; insolvability of the quintic; Galois's Great Theorem (solvability by 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, ruler-compass constructions, and the early history of Galois Theory. This book provides a concise introduction to Galois Theory suitable for first-year graduate students, either as a text for a course or for study outside the classroom. This new edition has been completely rewritten. Proofs are now clearer because more details are given and because the exposition has been reorganized (for example, the discussion of solvability by radicals now appears later in the book). The book now begins with a short section on symmetry groups of polygons in the plane, for there is an analogy between symmetry groups of polygons and Gaulois groups of polynomials. This analogy can serve as a guide to help readers organize the various field theoretic definitions and constructions. Several new theorems habe also been included; for example, the Casus Irreducibilis.".
- catalog extent "xiv, 157 p. ;".
- catalog identifier "0387985417 (softcover : alk. paper)".
- catalog isPartOf "Universitext".
- catalog issued "1998".
- catalog issued "c1998.".
- catalog language "eng".
- catalog publisher "New York : Springer,".
- catalog subject "512/.3 21".
- catalog subject "Galois theory.".
- catalog subject "Group theory.".
- catalog subject "Mathematics.".
- catalog subject "QA214 .R685 1998".
- catalog tableOfContents "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. Index.".
- catalog title "Galois theory / Joseph Rotman.".
- catalog type "text".