The Resource Abelian Groups and Representations of Finite Partially Ordered Sets, by David Arnold, (electronic resource)

Abelian Groups and Representations of Finite Partially Ordered Sets, by David Arnold, (electronic resource)

Label
Abelian Groups and Representations of Finite Partially Ordered Sets
Title
Abelian Groups and Representations of Finite Partially Ordered Sets
Statement of responsibility
by David Arnold
Creator
Author
Author
Subject
Language
  • eng
  • eng
Summary
A recurring theme in a traditional introductory graduate algebra course is the existence and consequences of relationships between different algebraic structures. This is also the theme of this book, an exposition of connections between representations of finite partially ordered sets and abelian groups. Emphasis is placed throughout on classification, a description of the objects up to isomorphism, and computation of representation type, a measure of when classification is feasible. David M. Arnold is the Ralph and Jean Storm Professor of Mathematics at Baylor University. He is the author of "Finite Rank Torsion Free Abelian Groups and Rings" published in the Springer-Verlag Lecture Notes in Mathematics series, a co-editor for two volumes of conference proceedings, and the author of numerous articles in mathematical research journals. His research interests are in abelian group theory and related topics, such as representations of partially ordered sets and modules over discrete valuation rings, subrings of algebraic number fields, and pullback rings. He received his Ph. D. from the University of Illinois, Urbana and was a member of the faculty at New Mexico State University for many years
Member of
http://library.link/vocab/creatorName
Arnold, David
Dewey number
512.2
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
qnRDA0JttMA
Image bit depth
0
Language note
English
LC call number
QA174-183
Literary form
non fiction
Nature of contents
dictionaries
Series statement
CMS Books in Mathematics, Ouvrages de mathématiques de la SMC,
http://library.link/vocab/subjectName
  • Group theory
  • Group Theory and Generalizations
Label
Abelian Groups and Representations of Finite Partially Ordered Sets, by David Arnold, (electronic resource)
Instantiates
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and indexes
Carrier category
online resource
Carrier category code
cr
Color
not applicable
Content category
text
Content type code
txt
Contents
1 Representations of Posets over a Field -- 1.1 Vector Spaces with Distinguished Subspaces -- 1.2 Representations of Posets and Matrix Problems -- 1.3 Finite Representation Type -- 1.4 Tame and Wild Representation Type -- 1.5 Generic Representations -- 2 Torsion-Free Abelian Groups -- 2.1 Quasi-isomorphism and Isomorphism at p -- 2.2 Near-isomorphism of Finite Rank Groups -- 2.3 Stable Range Conditions for Finite Rank Groups -- 2.4 Self-Small Groups and Endomorphism Rings -- 3 Butler Groups -- 3.1 Types and Completely Decomposable Groups -- 3.2 Characterizations of Finite Rank Groups -- 3.3 Quasi-isomorphism and ?-Representations of Posets -- 3.4 Countable Groups -- 3.5 Quasi-Generic Groups -- 4 Representations over a Discrete Valuation Ring -- 4.1 Finite and Rank-Finite Representation Type -- 4.2 Wild Modulo p Representation Type -- 4.3 Finite Rank Butler Groups and Isomorphism at p -- 5 Almost Completely Decomposable Groups -- 5.1 Characterizations and Properties -- 5.2 Isomorphism at p and Representation Type -- 5.3 Uniform Groups -- 5.4 Primary Regulating Quotient Groups -- 6 Representations over Fields and Exact Sequences -- 6.1 Projectives, Injectives, and Exact Sequences -- 6.2 Coxeter Correspondences -- 6.3 Almost Split Sequences -- 6.4 A Torsion Theory and Localizations -- 7 Finite Rank Butler Groups -- 7.1 Projectives, Injectives, and Exact Sequences -- 7.2 Endomorphism Rings -- 7.3 Bracket Groups -- 8 Applications of Representations and Butler Groups -- 8.1 Torsion-Free Modules over Discrete Valuation Rings -- 8.2 Finite Valuated Groups -- References -- List of Symbols -- Index of Terms
Dimensions
unknown
Edition
1st ed. 2000.
Extent
1 online resource (XII, 244 p.)
File format
multiple file formats
Form of item
online
Isbn
9781441987501
Level of compression
uncompressed
Media category
computer
Media type code
c
Other control number
10.1007/978-1-4419-8750-1
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000087748
  • (SSID)ssj0001295685
  • (PQKBManifestationID)11748624
  • (PQKBTitleCode)TC0001295685
  • (PQKBWorkID)11347074
  • (PQKB)11291730
  • (DE-He213)978-1-4419-8750-1
  • (MiAaPQ)EBC3074158
  • (EXLCZ)993400000000087748
Label
Abelian Groups and Representations of Finite Partially Ordered Sets, by David Arnold, (electronic resource)
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and indexes
Carrier category
online resource
Carrier category code
cr
Color
not applicable
Content category
text
Content type code
txt
Contents
1 Representations of Posets over a Field -- 1.1 Vector Spaces with Distinguished Subspaces -- 1.2 Representations of Posets and Matrix Problems -- 1.3 Finite Representation Type -- 1.4 Tame and Wild Representation Type -- 1.5 Generic Representations -- 2 Torsion-Free Abelian Groups -- 2.1 Quasi-isomorphism and Isomorphism at p -- 2.2 Near-isomorphism of Finite Rank Groups -- 2.3 Stable Range Conditions for Finite Rank Groups -- 2.4 Self-Small Groups and Endomorphism Rings -- 3 Butler Groups -- 3.1 Types and Completely Decomposable Groups -- 3.2 Characterizations of Finite Rank Groups -- 3.3 Quasi-isomorphism and ?-Representations of Posets -- 3.4 Countable Groups -- 3.5 Quasi-Generic Groups -- 4 Representations over a Discrete Valuation Ring -- 4.1 Finite and Rank-Finite Representation Type -- 4.2 Wild Modulo p Representation Type -- 4.3 Finite Rank Butler Groups and Isomorphism at p -- 5 Almost Completely Decomposable Groups -- 5.1 Characterizations and Properties -- 5.2 Isomorphism at p and Representation Type -- 5.3 Uniform Groups -- 5.4 Primary Regulating Quotient Groups -- 6 Representations over Fields and Exact Sequences -- 6.1 Projectives, Injectives, and Exact Sequences -- 6.2 Coxeter Correspondences -- 6.3 Almost Split Sequences -- 6.4 A Torsion Theory and Localizations -- 7 Finite Rank Butler Groups -- 7.1 Projectives, Injectives, and Exact Sequences -- 7.2 Endomorphism Rings -- 7.3 Bracket Groups -- 8 Applications of Representations and Butler Groups -- 8.1 Torsion-Free Modules over Discrete Valuation Rings -- 8.2 Finite Valuated Groups -- References -- List of Symbols -- Index of Terms
Dimensions
unknown
Edition
1st ed. 2000.
Extent
1 online resource (XII, 244 p.)
File format
multiple file formats
Form of item
online
Isbn
9781441987501
Level of compression
uncompressed
Media category
computer
Media type code
c
Other control number
10.1007/978-1-4419-8750-1
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000087748
  • (SSID)ssj0001295685
  • (PQKBManifestationID)11748624
  • (PQKBTitleCode)TC0001295685
  • (PQKBWorkID)11347074
  • (PQKB)11291730
  • (DE-He213)978-1-4419-8750-1
  • (MiAaPQ)EBC3074158
  • (EXLCZ)993400000000087748

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