The Resource Galois Theory, by Joseph Rotman, (electronic resource)

Galois Theory, by Joseph Rotman, (electronic resource)

Label
Galois Theory
Title
Galois Theory
Statement of responsibility
by Joseph Rotman
Creator
Author
Author
Subject
Language
  • eng
  • eng
Summary
The 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
Member of
http://library.link/vocab/creatorName
Rotman, Joseph
Dewey number
512/.3
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
QAIGGmhlNN8
Image bit depth
0
Language note
English
LC call number
QA174-183
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Universitext,
http://library.link/vocab/subjectName
  • Group theory
  • Group Theory and Generalizations
Label
Galois Theory, by Joseph Rotman, (electronic resource)
Instantiates
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Color
not applicable
Content category
text
Content type code
  • txt
Contents
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
Dimensions
unknown
Edition
Second Edition.
Extent
1 online resource (XIV, 176 p.)
File format
multiple file formats
Form of item
online
Isbn
9781461206170
Level of compression
uncompressed
Media category
computer
Media type code
  • c
Other control number
10.1007/978-1-4612-0617-0
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000089202
  • (SSID)ssj0000806402
  • (PQKBManifestationID)11956323
  • (PQKBTitleCode)TC0000806402
  • (PQKBWorkID)10766420
  • (PQKB)10836309
  • (DE-He213)978-1-4612-0617-0
  • (MiAaPQ)EBC3074090
  • (EXLCZ)993400000000089202
Label
Galois Theory, by Joseph Rotman, (electronic resource)
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Color
not applicable
Content category
text
Content type code
  • txt
Contents
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
Dimensions
unknown
Edition
Second Edition.
Extent
1 online resource (XIV, 176 p.)
File format
multiple file formats
Form of item
online
Isbn
9781461206170
Level of compression
uncompressed
Media category
computer
Media type code
  • c
Other control number
10.1007/978-1-4612-0617-0
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000089202
  • (SSID)ssj0000806402
  • (PQKBManifestationID)11956323
  • (PQKBTitleCode)TC0000806402
  • (PQKBWorkID)10766420
  • (PQKB)10836309
  • (DE-He213)978-1-4612-0617-0
  • (MiAaPQ)EBC3074090
  • (EXLCZ)993400000000089202

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