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AuthorRotman, Joseph. author
TitleGalois Theory [electronic resource] / by Joseph Rotman
ImprintNew York, NY : Springer US, 1990
Connect tohttp://dx.doi.org/10.1007/978-1-4684-0367-1
Descript XII, 112 p. online resource

SUMMARY

J***VERKAUFSKATEGORIE*** 0 e 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


CONTENT

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 -- Galoisโ{128}{153}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


Mathematics Group theory Mathematics Group Theory and Generalizations



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