Galois Theory

Joseph Rotman (Autor)

Buch | Softcover

108 Seiten

1994
Springer-Verlag New York Inc.
978-0-387-97305-0 (ISBN)

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Galois Theory

Joseph Rotman

1998

Buch | Softcover

58, ⁸⁴ €

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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.

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.

Erscheint lt. Verlag	6.12.1994
Reihe/Serie	Universitext
Zusatzinfo	XII, 108 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik
ISBN-10	0-387-97305-2 / 0387973052
ISBN-13	978-0-387-97305-0 / 9780387973050
Zustand	Neuware