The Resource A guide to groups, rings, and fields, Fernando Q. Gouvêa, (electronic resource)

A guide to groups, rings, and fields, Fernando Q. Gouvêa, (electronic resource)

Label
A guide to groups, rings, and fields
Title
A guide to groups, rings, and fields
Statement of responsibility
Fernando Q. Gouvêa
Creator
Subject
Genre
Language
  • eng
  • eng
Summary
This Guide offers a concise overview of the theory of groups, rings, and fields at the graduate level, emphasizing those aspects that are useful in other parts of mathematics. It focuses on the main ideas and how they hang together. It will be useful to both students and professionals. In addition to the standard material on groups, rings, modules, fields, and Galois theory, the book includes discussions of other important topics that are often omitted in the standard graduate course, including linear groups, group representations, the structure of Artinian rings, projective, injective and flat modules, Dedekind domains, and central simple algebras. All of the important theorems are discussed, without proofs but often with a discussion of the intuitive ideas behind those proofs. Those looking for a way to review and refresh their basic algebra will benefit from reading this Guide, and it will also serve as a ready reference for mathematicians who make use of algebra in their work
Member of
Cataloging source
MiAaPQ
http://library.link/vocab/creatorName
Gouvêa, Fernando Q.
Dewey number
512
Illustrations
illustrations
Index
index present
Language note
English
LC call number
QA155
LC item number
.G68 2012
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
  • Dolciani mathematical expositions
  • MAA guides
  • Dolciani Mathematical Expositions
Series volume
  • no. 48
  • no. 8
  • v.48
http://library.link/vocab/subjectName
  • Algebra
  • Rings (Algebra)
  • Algebraic fields
Label
A guide to groups, rings, and fields, Fernando Q. Gouvêa, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. 277-283) and indexes
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
  • ""copyright page ""; ""title page ""; ""Contents""; ""Preface""; ""A Guide to this Guide""; ""Algebra: Classical, Modern, and Ultramodern""; ""The Beginnings of Modern Algebra""; ""Modern Algebra""; ""Ultramodern Algebra""; ""What Next?""; ""Categories""; ""Categories""; ""Functors""; ""Natural Transformations""; ""Products, Coproducts, and Generalizations""; ""Algebraic Structures""; ""Structures with One Operation""; ""Rings""; ""Actions""; ""Semirings""; ""Algebras""; ""Ordered Structures""; ""Groups and their Representations""; ""Definitions""; ""Groups and homomorphisms""; ""Subgroups""
  • ""Finitely generated groups and the Burnside problem""""Other nice subgroups""; ""Conjugation and the class equation""; ""p-groups""; ""Sylow's Theorem and Sylow subgroups""; ""Sequences of Subgroups""; ""Composition series""; ""Central series, derived series, nilpotent, solvable""; ""New Groups from Old""; ""Direct products""; ""Semidirect products""; ""Isometries of R3""; ""Free products""; ""Direct sums of abelian groups""; ""Inverse limits and direct limits""; ""Generators and Relations""; ""Definition and examples""; ""Cayley graphs""; ""The word problem""; ""Abelian Groups""
  • ""Torsion""""The structure theorem""; ""Small Groups""; ""Order four, order p2""; ""Order six, order pq""; ""Order eight, order p3""; ""And so on""; ""Groups of Permutations""; ""Cycle notation and cycle structure""; ""Conjugation and cycle structure""; ""Transpositions as generators""; ""Signs and the alternating groups""; ""Transitive subgroups""; ""Automorphism group of S_n""; ""Some Linear Groups""; ""Definitions and examples""; ""Generators""; ""The regular representation""; ""Diagonal and upper triangular""; ""Normal subgroups""; ""PGL""; ""Linear groups over finite fields""
  • ""Representations of Finite Groups""""Definitions""; ""Examples""; ""Constructions""; ""Decomposing into irreducibles""; ""Direct products""; ""Characters""; ""Character tables""; ""Going through quotients""; ""Going up and down""; ""Representations of S_4""; ""Rings and Modules""; ""Definitions""; ""Rings""; ""Modules""; ""Torsion""; ""Bimodules""; ""Ideals""; ""Restriction of scalars""; ""Rings with few ideals""; ""More Examples, More Definitions""; ""The integers""; ""Fields and skew fields""; ""Polynomials""; ""R-algebras""; ""Matrix rings""; ""Group algebras""; ""Monsters""
  • ""Some examples of modules""
Dimensions
unknown
Extent
1 online resource (328 p.)
Form of item
online
Isbn
9781614442110
Media category
computer
Media type code
c
Specific material designation
remote
System control number
  • (CKB)2670000000330035
  • (EBL)3330368
  • (SSID)ssj0000788991
  • (PQKBManifestationID)11441484
  • (PQKBTitleCode)TC0000788991
  • (PQKBWorkID)10725850
  • (PQKB)10798453
  • (UkCbUP)CR9781614442110
  • (MiAaPQ)EBC3330368
  • (EXLCZ)992670000000330035
Label
A guide to groups, rings, and fields, Fernando Q. Gouvêa, (electronic resource)
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. 277-283) and indexes
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
  • ""copyright page ""; ""title page ""; ""Contents""; ""Preface""; ""A Guide to this Guide""; ""Algebra: Classical, Modern, and Ultramodern""; ""The Beginnings of Modern Algebra""; ""Modern Algebra""; ""Ultramodern Algebra""; ""What Next?""; ""Categories""; ""Categories""; ""Functors""; ""Natural Transformations""; ""Products, Coproducts, and Generalizations""; ""Algebraic Structures""; ""Structures with One Operation""; ""Rings""; ""Actions""; ""Semirings""; ""Algebras""; ""Ordered Structures""; ""Groups and their Representations""; ""Definitions""; ""Groups and homomorphisms""; ""Subgroups""
  • ""Finitely generated groups and the Burnside problem""""Other nice subgroups""; ""Conjugation and the class equation""; ""p-groups""; ""Sylow's Theorem and Sylow subgroups""; ""Sequences of Subgroups""; ""Composition series""; ""Central series, derived series, nilpotent, solvable""; ""New Groups from Old""; ""Direct products""; ""Semidirect products""; ""Isometries of R3""; ""Free products""; ""Direct sums of abelian groups""; ""Inverse limits and direct limits""; ""Generators and Relations""; ""Definition and examples""; ""Cayley graphs""; ""The word problem""; ""Abelian Groups""
  • ""Torsion""""The structure theorem""; ""Small Groups""; ""Order four, order p2""; ""Order six, order pq""; ""Order eight, order p3""; ""And so on""; ""Groups of Permutations""; ""Cycle notation and cycle structure""; ""Conjugation and cycle structure""; ""Transpositions as generators""; ""Signs and the alternating groups""; ""Transitive subgroups""; ""Automorphism group of S_n""; ""Some Linear Groups""; ""Definitions and examples""; ""Generators""; ""The regular representation""; ""Diagonal and upper triangular""; ""Normal subgroups""; ""PGL""; ""Linear groups over finite fields""
  • ""Representations of Finite Groups""""Definitions""; ""Examples""; ""Constructions""; ""Decomposing into irreducibles""; ""Direct products""; ""Characters""; ""Character tables""; ""Going through quotients""; ""Going up and down""; ""Representations of S_4""; ""Rings and Modules""; ""Definitions""; ""Rings""; ""Modules""; ""Torsion""; ""Bimodules""; ""Ideals""; ""Restriction of scalars""; ""Rings with few ideals""; ""More Examples, More Definitions""; ""The integers""; ""Fields and skew fields""; ""Polynomials""; ""R-algebras""; ""Matrix rings""; ""Group algebras""; ""Monsters""
  • ""Some examples of modules""
Dimensions
unknown
Extent
1 online resource (328 p.)
Form of item
online
Isbn
9781614442110
Media category
computer
Media type code
c
Specific material designation
remote
System control number
  • (CKB)2670000000330035
  • (EBL)3330368
  • (SSID)ssj0000788991
  • (PQKBManifestationID)11441484
  • (PQKBTitleCode)TC0000788991
  • (PQKBWorkID)10725850
  • (PQKB)10798453
  • (UkCbUP)CR9781614442110
  • (MiAaPQ)EBC3330368
  • (EXLCZ)992670000000330035

Library Locations

  • Albert D. Cohen Management LibraryBorrow it
    181 Freedman Crescent, Winnipeg, MB, R3T 5V4, CA
    49.807878 -97.129961
  • Architecture/Fine Arts LibraryBorrow it
    84 Curry Place, Winnipeg, MB, CA
    49.807716 -97.136226
  • Archives and Special CollectionsBorrow it
    25 Chancellors Circle (Elizabeth Dafoe Library), Room 330, Winnipeg, MB, R3T 2N2, CA
    49.809961 -97.131878
  • Bibliothèque Alfred-Monnin (Université de Saint-Boniface)Borrow it
    200, avenue de la Cathédrale, Local 2110, Winnipeg, MB, R2H 0H7, CA
    49.888861 -97.119735
  • Bill Larson Library (Grace Hospital)Borrow it
    300 Booth Drive, G-227, Winnipeg, MB, R3J 3M7, CA
    49.882400 -97.276436
  • Carolyn Sifton - Helene Fuld Library (St. Boniface General Hospital)Borrow it
    409 Tache Avenue, Winnipeg, MB, R2H 2A6, CA
    49.883388 -97.126050
  • Concordia Hospital LibraryBorrow it
    1095 Concordia Avenue, Winnipeg, MB, R2K 3S8, CA
    49.913252 -97.064683
  • Donald W. Craik Engineering LibraryBorrow it
    75B Chancellors Circle (Engineering Building E3), Room 361, Winnipeg, MB, R3T 2N2, CA
    49.809053 -97.133292
  • E.K. Williams Law LibraryBorrow it
    224 Dysart Road, Winnipeg, MB, R3T 5V4, CA
    49.811829 -97.131017
  • Eckhardt-Gramatté Music LibraryBorrow it
    136 Dafoe Road (Taché Arts Complex), Room 257, Winnipeg, MB, R3T 2N2, CA
    49.807964 -97.132222
  • Elizabeth Dafoe LibraryBorrow it
    25 Chancellors Circle, Winnipeg, MB, R3T 2N2, CA
    49.809961 -97.131878
  • Fr. H. Drake Library (St. Paul's College)Borrow it
    70 Dysart Road, Winnipeg, MB, R3T 2M6, CA
    49.810605 -97.138184
  • J.W. Crane Memorial Library (Deer Lodge Centre)Borrow it
    2109 Portage Avenue, Winnipeg, MB, R3J 0L3, CA
    49.878000 -97.235520
  • Libraries Annex (not open to the public; please see web page for details)Borrow it
    25 Chancellors Circle (in the Elizabeth Dafoe Library), Winnipeg, MB, R3T 2N2, CA
    49.809961 -97.131878
  • Neil John Maclean Health Sciences LibraryBorrow it
    727 McDermot Avenue (Brodie Centre), 200 Level, Winnipeg, MB, R3E 3P5, CA
    49.903563 -97.160554
  • Sciences and Technology LibraryBorrow it
    186 Dysart Road, Winnipeg, MB, R3T 2M8, CA
    49.811526 -97.133257
  • Seven Oaks General Hospital LibraryBorrow it
    2300 McPhillips Street, Winnipeg, MB, R2V 3M3, CA
    49.955177 -97.148865
  • Sister St. Odilon Library (Misericordia Health Centre)Borrow it
    99 Cornish Avenue, Winnipeg, MB, R3C 1A2, CA
    49.879592 -97.160425
  • St. John's College LibraryBorrow it
    92 Dysart Road, Winnipeg, MB, R3T 2M5, CA
    49.811242 -97.137156
  • Victoria General Hospital LibraryBorrow it
    2340 Pembina Highway, Winnipeg, MB, R3T 2E8, CA
    49.806755 -97.152739
  • William R Newman Library (Agriculture)Borrow it
    66 Dafoe Road, Winnipeg, MB, R3T 2R3, CA
    49.806936 -97.135525
Processing Feedback ...