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Autore: |
Rotman Joseph
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Titolo: |
Galois Theory [[electronic resource] /] / by Joseph Rotman
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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 |
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.: | 9910789215203321 |
Lo trovi qui: | Univ. Federico II |
Opac: | Controlla la disponibilitĂ qui |