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[null,"1.","Record Nr.",null,"UNINA9910789215203321"]
[null,null,"Autore",null,"Rotman Joseph"]
[null,null,"Titolo",null,"Galois Theory [[electronic resource] /] / by Joseph Rotman"]
[null,null,"Pubbl/distr/stampa",null,"New York, NY : , : Springer New York : , : Imprint : Springer, , 1990"]
[null,null,"ISBN",null,"1-4684-0367-2"]
[null,null,"Edizione",null,"[1st ed. 1990.]"]
[null,null,"Descrizione fisica",null,"1 online resource (XII, 112 p.)"]
[null,null,"Collana",null,"Universitext, , 0172-5939"]
[null,null,"Classificazione",null,"12F10"]
[null,null,"Disciplina",null,"512/.3"]
[null,null,"Soggetti",null,"Group theory"]
[{"$nulls":4},"Group Theory and Generalizations"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","Bibliographic Level Mode of Issuance: Monograph"]
[null,null,null,"Nota di bibliografia","Includes bibliographical references and index."]
[null,null,"Nota di contenuto",null,"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."]
[null,null,null,"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."]