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121227s1998 nyua o 000 0 eng d |
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|a 9781461206170 (electronic bk.)
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| 020 |
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|a 1461206170 (electronic bk.)
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|a (OCoLC)840277883
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|a Rotman, Joseph.
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| 245 |
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|a Galois Theory /
|c by Joseph Rotman.
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| 250 |
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|a Second edition.
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| 264 |
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1 |
|a New York, NY :
|b Springer New York :
|b Imprint :
|b Springer,
|c 1998.
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| 300 |
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|a 1 online resource (XIV, 176 pages 9 illustrations)
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| 336 |
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|a text
|b txt
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| 337 |
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|a computer
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|2 rdamedia
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| 338 |
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|a online resource
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| 490 |
0 |
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|a Universitext, 0172-5939
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| 505 |
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|a Symmetry -- Rings -- Domains and Fields -- Homomorphisms and Ideals -- Quotient Rings -- Polynomial Rings over Fields -- Prime Ideals and Maximal Ideals -- Irreducible Polynomials -- Classical Formulas -- Splitting Fields -- The Galois Group -- Roots of Unity -- Solvability by Radicals -- Independence of Characters -- Galois Extensions -- The Fundamental Theorem of Galois Theory -- Applications -- Galois's Great Theorem -- Discriminants -- Galois Groups of Quadratics, Cubics, and Quartics -- Epilogue -- Appendix A: Group Theory Dictionary -- Appendix B: Group Theory Used in the Text -- Appendix C: Ruler-Compass Constructions -- Appendix D: Old-fashioned Galois Theory -- References. Index.
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| 520 |
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|a This text offers a clear, efficient exposition of Galois Theory with complete proofs and exercises. Topics include: cubic and quartic formulas; Fundamental Theory of Galois Theory; insolvability of the quintic; Galois's Great Theorem (solvability by radicals of a polynomial is equivalent to solvability of its Galois Group); and computation of Galois groups of cubics and quartics. There are appendices on group theory, ruler-compass constructions, and the early history of Galois Theory. This book provides a concise introduction to Galois Theory suitable for first-year graduate students, either as a text for a course or for study outside the classroom. This new edition has been completely rewritten. Proofs are now clearer because more details are given and because the exposition has been reorganized (for example, the discussion of solvability by radicals now appears later in the book). The book now begins with a short section on symmetry groups of polygons in the plane, for there is an analogy between symmetry groups of polygons and Gaulois groups of polynomials. This analogy can serve as a guide to help readers organize the various field theoretic definitions and constructions. Several new theorems habe also been included; for example, the Casus Irreducibilis.
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| 500 |
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|a Electronic resource.
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| 650 |
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|a Mathematics.
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| 650 |
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|a Group theory.
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| 650 |
|
7 |
|a Group theory.
|2 fast
|0 (OCoLC)fst00948521
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| 650 |
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|a Mathematics.
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|0 (OCoLC)fst01012163
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| 655 |
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|a Electronic books.
|2 local
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| 710 |
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|a SpringerLink (Online service)
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|u http://proxy.library.tamu.edu/login?url=https://link.springer.com/10.1007/978-1-4612-0617-0
|z Connect to the full text of this electronic book
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|a Texas A&M University
|b College Station
|c Electronic Resources
|s www_evans
|d Available Online
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|e QA174-183
|h Library of Congress classification
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| 998 |
f |
f |
|a QA174-183
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|l Available Online
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