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The Resource Abelian Groups, by László Fuchs, (electronic resource)

Abelian Groups, by László Fuchs, (electronic resource)

Creator
Author
Contributor
Summary
Written by one of the subject's foremost experts, this book focuses on the central developments and modern methods of the advanced theory of abelian groups, while remaining accessible, as an introduction and reference, to the non-specialist. It provides a coherent source for results scattered throughout the research literature with lots of new proofs. The presentation highlights major trends that have radically changed the modern character of the subject, in particular, the use of homological methods in the structure theory of various classes of abelian groups, and the use of advanced set-theoretical methods in the study of undecidability problems. The treatment of the latter trend includes Shelah's seminal work on the undecidability in ZFC of Whitehead's Problem; while the treatment of the former trend includes an extensive (but non-exhaustive) study of p-groups, torsion-free groups, mixed groups, and important classes of groups arising from ring theory. To prepare the reader to tackle these topics, the book reviews the fundamentals of abelian group theory and provides some background material from category theory, set theory, topology, and homological algebra. An abundance of exercises are included to test the reader's comprehension, and to explore noteworthy extensions and related sidelines of the main topics. A list of open problems and questions, in each chapter, invite the reader to take an active part in the subject's further development
Language
eng
Work
Publication
Edition
1st ed. 2015.
Extent
XXI, 747 p.
Contents
  • Fundamentals
  • Direct Sums
  • Direct Sums of Cyclic Groups
  • Divisibility and Injectivity
  • Purity and Basic Subgroups
  • Algebraically Compact Groups
  • Homomorphism Groups
  • Tensor and Torsion Products
  • Groups of Extensions and Cotorsion Groups
  • Torsion Groups
  • p-Groups with Elements of Infinite Height
  • Torsion-free Groups
  • Torsion-free Groups of Infinite Rank
  • Butler Groups
  • Mixed Groups
  • Endomorphism Rings
  • Automorphism groups
  • Groups in Rings and in Fields
Isbn
9783319194226
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-319-19422-6
Instance
Label
Abelian Groups
Title
Abelian Groups
Statement of responsibility
by László Fuchs
Creator
Contributor
Author
Subject
Language
eng
Summary
Written by one of the subject's foremost experts, this book focuses on the central developments and modern methods of the advanced theory of abelian groups, while remaining accessible, as an introduction and reference, to the non-specialist. It provides a coherent source for results scattered throughout the research literature with lots of new proofs. The presentation highlights major trends that have radically changed the modern character of the subject, in particular, the use of homological methods in the structure theory of various classes of abelian groups, and the use of advanced set-theoretical methods in the study of undecidability problems. The treatment of the latter trend includes Shelah's seminal work on the undecidability in ZFC of Whitehead's Problem; while the treatment of the former trend includes an extensive (but non-exhaustive) study of p-groups, torsion-free groups, mixed groups, and important classes of groups arising from ring theory. To prepare the reader to tackle these topics, the book reviews the fundamentals of abelian group theory and provides some background material from category theory, set theory, topology, and homological algebra. An abundance of exercises are included to test the reader's comprehension, and to explore noteworthy extensions and related sidelines of the main topics. A list of open problems and questions, in each chapter, invite the reader to take an active part in the subject's further development
Member of
http://library.link/vocab/creatorName
Fuchs, László
Image bit depth
0
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
SpringerLink (Online service)
Series statement
Springer Monographs in Mathematics,
http://library.link/vocab/subjectName
  • Mathematics
  • Category theory (Mathematics)
  • Homological algebra
  • Commutative algebra
  • Commutative rings
  • Group theory
Label
Abelian Groups, by László Fuchs, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-319-19422-6
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Contents
Fundamentals -- Direct Sums -- Direct Sums of Cyclic Groups -- Divisibility and Injectivity -- Purity and Basic Subgroups -- Algebraically Compact Groups -- Homomorphism Groups -- Tensor and Torsion Products -- Groups of Extensions and Cotorsion Groups -- Torsion Groups -- p-Groups with Elements of Infinite Height -- Torsion-free Groups -- Torsion-free Groups of Infinite Rank -- Butler Groups -- Mixed Groups -- Endomorphism Rings -- Automorphism groups -- Groups in Rings and in Fields
Control code
978-3-319-19422-6
Dimensions
unknown
Edition
1st ed. 2015.
Extent
XXI, 747 p.
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319194226
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-3-319-19422-6
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)937551553
Label
Abelian Groups, by László Fuchs, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-319-19422-6
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Contents
Fundamentals -- Direct Sums -- Direct Sums of Cyclic Groups -- Divisibility and Injectivity -- Purity and Basic Subgroups -- Algebraically Compact Groups -- Homomorphism Groups -- Tensor and Torsion Products -- Groups of Extensions and Cotorsion Groups -- Torsion Groups -- p-Groups with Elements of Infinite Height -- Torsion-free Groups -- Torsion-free Groups of Infinite Rank -- Butler Groups -- Mixed Groups -- Endomorphism Rings -- Automorphism groups -- Groups in Rings and in Fields
Control code
978-3-319-19422-6
Dimensions
unknown
Edition
1st ed. 2015.
Extent
XXI, 747 p.
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319194226
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-3-319-19422-6
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)937551553

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