03046nam 22005175 450 991048041600332120200704112822.01-4684-0367-210.1007/978-1-4684-0367-1(CKB)3400000000097389(SSID)ssj0000806401(PQKBManifestationID)11498250(PQKBTitleCode)TC0000806401(PQKBWorkID)10748768(PQKB)10070274(DE-He213)978-1-4684-0367-1(MiAaPQ)EBC3082868(PPN)237999803(EXLCZ)99340000000009738920121227d1990 u| 0engurnn|008mamaatxtccrGalois Theory[electronic resource] /by Joseph Rotman1st ed. 1990.New York, NY :Springer New York :Imprint: Springer,1990.1 online resource (XII, 112 p.) Universitext,0172-5939Bibliographic Level Mode of Issuance: Monograph0-387-97305-2 Includes bibliographical references and index.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.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.Universitext,0172-5939Group theoryGroup Theory and Generalizationshttps://scigraph.springernature.com/ontologies/product-market-codes/M11078Group theory.Group Theory and Generalizations.512/.3Rotman Josephauthttp://id.loc.gov/vocabulary/relators/aut350470BOOK9910480416003321Galois theory374562UNINA