LEADER 03046nam 22005175 450 001 9910480416003321 005 20200704112822.0 010 $a1-4684-0367-2 024 7 $a10.1007/978-1-4684-0367-1 035 $a(CKB)3400000000097389 035 $a(SSID)ssj0000806401 035 $a(PQKBManifestationID)11498250 035 $a(PQKBTitleCode)TC0000806401 035 $a(PQKBWorkID)10748768 035 $a(PQKB)10070274 035 $a(DE-He213)978-1-4684-0367-1 035 $a(MiAaPQ)EBC3082868 035 $a(PPN)237999803 035 $a(EXLCZ)993400000000097389 100 $a20121227d1990 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aGalois Theory$b[electronic resource] /$fby Joseph Rotman 205 $a1st ed. 1990. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1990. 215 $a1 online resource (XII, 112 p.) 225 1 $aUniversitext,$x0172-5939 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a0-387-97305-2 320 $aIncludes bibliographical references and index. 327 $aRings -- 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. 330 $aThis text offers a clear, efficient exposition of Galois Theory with exercises and complete proofs. Topics include: Cardano's formulas; the Fundamental Theorem; Galois' Great Theorem (solvability for radicals of a polynomial is equivalent to solvability of its Galois Group); and computation of Galois group of cubics and quartics. There are appendices on group theory and on ruler-compass constructions. Developed on the basis of a second-semester graduate algebra course, following a course on group theory, this book will provide a concise introduction to Galois Theory suitable for graduate students, either as a text for a course or for study outside the classroom. 410 0$aUniversitext,$x0172-5939 606 $aGroup theory 606 $aGroup Theory and Generalizations$3https://scigraph.springernature.com/ontologies/product-market-codes/M11078 615 0$aGroup theory. 615 14$aGroup Theory and Generalizations. 676 $a512/.3 700 $aRotman$b Joseph$4aut$4http://id.loc.gov/vocabulary/relators/aut$0350470 906 $aBOOK 912 $a9910480416003321 996 $aGalois theory$9374562 997 $aUNINA