LEADER 03384nam 22005175 450 001 9910480378503321 005 20200704114045.0 010 $a1-4612-0617-0 024 7 $a10.1007/978-1-4612-0617-0 035 $a(CKB)3400000000089202 035 $a(SSID)ssj0000806402 035 $a(PQKBManifestationID)11956323 035 $a(PQKBTitleCode)TC0000806402 035 $a(PQKBWorkID)10766420 035 $a(PQKB)10836309 035 $a(DE-He213)978-1-4612-0617-0 035 $a(MiAaPQ)EBC3074090 035 $a(PPN)238006115 035 $a(EXLCZ)993400000000089202 100 $a20121227d1998 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 $a2nd ed. 1998. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1998. 215 $a1 online resource (XIV, 176 p.) 225 1 $aUniversitext,$x0172-5939 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a0-387-98541-7 320 $aIncludes bibliographical references and index. 327 $aSymmetry -- 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. 330 $aThe first edition aimed to give a geodesic path to the Fundamental Theorem of Galois Theory, and I still think its brevity is valuable. Alas, the book is now a bit longer, but I feel that the changes are worthwhile. I began by rewriting almost all the text, trying to make proofs clearer, and often giving more details than before. Since many students find the road to the Fundamental Theorem an intricate one, the book now begins with a short section on symmetry groups of polygons in the plane; an analogy of polygons and their symmetry groups with polynomials and their Galois groups can serve as a guide by helping readers organize the various definitions and constructions. The exposition has been reorganized so that the discussion of solvability by radicals now appears later; this makes the proof of the Abel-Ruffini theo rem easier to digest. I have also included several theorems not in the first edition. For example, the Casus Irreducibilis is now proved, in keeping with a historical interest lurking in these pages. 410 0$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 $a9910480378503321 996 $aGalois theory$9374562 997 $aUNINA