The Resource Introduction to the Galois Correspondence, by Maureen H. Fenrick, (electronic resource)

Introduction to the Galois Correspondence, by Maureen H. Fenrick, (electronic resource)

Label
Introduction to the Galois Correspondence
Title
Introduction to the Galois Correspondence
Statement of responsibility
by Maureen H. Fenrick
Creator
Author
Author
Subject
Language
  • eng
  • eng
Summary
In this presentation of the Galois correspondence, modern theories of groups and fields are used to study problems, some of which date back to the ancient Greeks. The techniques used to solve these problems, rather than the solutions themselves, are of primary importance. The ancient Greeks were concerned with constructibility problems. For example, they tried to determine if it was possible, using straightedge and compass alone, to perform any of the following tasks? (1) Double an arbitrary cube; in particular, construct a cube with volume twice that of the unit cube. (2) Trisect an arbitrary angle. (3) Square an arbitrary circle; in particular, construct a square with area 1r. (4) Construct a regular polygon with n sides for n > 2. If we define a real number c to be constructible if, and only if, the point (c, 0) can be constructed starting with the points (0,0) and (1,0), then we may show that the set of constructible numbers is a subfield of the field R of real numbers containing the field Q of rational numbers. Such a subfield is called an intermediate field of Rover Q. We may thus gain insight into the constructibility problems by studying intermediate fields of Rover Q. In chapter 4 we will show that (1) through (3) are not possible and we will determine necessary and sufficient conditions that the integer n must satisfy in order that a regular polygon with n sides be constructible
http://library.link/vocab/creatorName
Fenrick, Maureen H
Dewey number
512.2
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
N6PSTq8QRp8
Image bit depth
0
Language note
English
LC call number
QA174-183
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/subjectName
  • Group theory
  • Field theory (Physics)
  • Algebra
  • Group Theory and Generalizations
  • Field Theory and Polynomials
  • Algebra
Label
Introduction to the Galois Correspondence, by Maureen H. Fenrick, (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
I. Preliminaries - Groups and Rings -- 1. Introduction to Groups -- 2. Quotient Groups and Sylow Subgroups -- 3. Finite Abelian Groups and Solvable Groups -- 4. Introduction to Rings -- 5. Factoring in F[x] -- II. Field Extensions -- 1. Simple Extensions -- 2. Algebraic Extensions -- 3. Splitting Fields and Normal Extensions -- III. The Galois Correspondence -- 1. The Fundamental Correspondence -- 2. The Solvable Correspondence -- IV. Applications -- 1. Constructibility -- 2. Roots of Unity -- 3. Wedderburn’s Theorem -- 3. Dirichlet’s Theorem and Finite Abelian Groups -- Appendix A - Groups -- 1. Group Actions and the Sylow Theorems -- 2. Free Groups, Generators and Relations -- Appendix B - Factoring in Integral Domains -- 1. Euclidean Domains and Principal Ideal Domains -- 2. Prime and Irreducible Elements -- 3. Unique Factorization Domains -- Appendix C - Vector Spaces -- 1. Subspaces, Linear Independence and Spanning -- 2. Bases and Dimension
Dimensions
unknown
Edition
Second Edition.
Extent
1 online resource (XI, 244 p.)
File format
multiple file formats
Form of item
online
Isbn
9781461217923
Level of compression
uncompressed
Media category
computer
Media type code
c
Other control number
10.1007/978-1-4612-1792-3
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000089705
  • (SSID)ssj0001297271
  • (PQKBManifestationID)11986982
  • (PQKBTitleCode)TC0001297271
  • (PQKBWorkID)11362487
  • (PQKB)10561499
  • (DE-He213)978-1-4612-1792-3
  • (MiAaPQ)EBC3076418
  • (EXLCZ)993400000000089705
Label
Introduction to the Galois Correspondence, by Maureen H. Fenrick, (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
I. Preliminaries - Groups and Rings -- 1. Introduction to Groups -- 2. Quotient Groups and Sylow Subgroups -- 3. Finite Abelian Groups and Solvable Groups -- 4. Introduction to Rings -- 5. Factoring in F[x] -- II. Field Extensions -- 1. Simple Extensions -- 2. Algebraic Extensions -- 3. Splitting Fields and Normal Extensions -- III. The Galois Correspondence -- 1. The Fundamental Correspondence -- 2. The Solvable Correspondence -- IV. Applications -- 1. Constructibility -- 2. Roots of Unity -- 3. Wedderburn’s Theorem -- 3. Dirichlet’s Theorem and Finite Abelian Groups -- Appendix A - Groups -- 1. Group Actions and the Sylow Theorems -- 2. Free Groups, Generators and Relations -- Appendix B - Factoring in Integral Domains -- 1. Euclidean Domains and Principal Ideal Domains -- 2. Prime and Irreducible Elements -- 3. Unique Factorization Domains -- Appendix C - Vector Spaces -- 1. Subspaces, Linear Independence and Spanning -- 2. Bases and Dimension
Dimensions
unknown
Edition
Second Edition.
Extent
1 online resource (XI, 244 p.)
File format
multiple file formats
Form of item
online
Isbn
9781461217923
Level of compression
uncompressed
Media category
computer
Media type code
c
Other control number
10.1007/978-1-4612-1792-3
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000089705
  • (SSID)ssj0001297271
  • (PQKBManifestationID)11986982
  • (PQKBTitleCode)TC0001297271
  • (PQKBWorkID)11362487
  • (PQKB)10561499
  • (DE-He213)978-1-4612-1792-3
  • (MiAaPQ)EBC3076418
  • (EXLCZ)993400000000089705

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