Galois Theory / / by Joseph Rotman

• Autore: Rotman Joseph
• Pubblicazione: New York, NY : , : Springer New York : , : Imprint : Springer, , 1990
• Edizione: 1st ed. 1990.
• Descrizione fisica: 1 online resource (XII, 112 p.)
• Disciplina: 512/.3; 512.3
• Soggetto topico: Group theory; Group Theory and Generalizations
• Classificazione: 12F10
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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.
• Sommario/riassunto: 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.
• Titolo autorizzato: Galois theory
• ISBN: 1-4684-0367-2
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910818053903321
• Lo trovi qui: Univ. Federico II
• Serie: Universitext, . 0172-5939