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Abelian Groups and Representations of Finite Partially Ordered Sets : Cms Advanced Books in Mathematics - David Arnold

Abelian Groups and Representations of Finite Partially Ordered Sets

Cms Advanced Books in Mathematics

Hardcover Published: 16th June 2000
ISBN: 9780387989822
Number Of Pages: 244

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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.

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"The book provides a rich source or a variety of readers. As noted above, it offers an excellent and much-needed introduction to the subject of representations of posets. It could readily be used for a second year graduate course in algebra, with many tools and suggestions for cutting edge research. Finally, it is a handy reference for anyone interested in the study of torsion-free abelian groups of finite rank or related questions in representations of posets. If writing this review had not put a free copy on my bookshelf, I would rush to the web to order one."

Preface
Representations of Posets over a Fieldp. 1
Vector Spaces with Distinguished Subspacesp. 1
Representations of Posets and Matrix Problemsp. 10
Finite Representation Typep. 19
Tame and Wild Representation Typep. 31
Generic Representationsp. 39
Torsion-Free Abelian Groupsp. 47
Quasi-isomorphism and Isomorphism at pp. 47
Near-isomorphism of Finite Rank Groupsp. 56
Stable Range Conditions for Finite Rank Groupsp. 62
Self-Small Groups and Endomorphism Ringsp. 69
Butler Groupsp. 76
Types and Completely Decomposable Groupsp. 76
Characterizations of Finite Rank Groupsp. 88
Quasi-isomorphism and Q-Representations of Posetsp. 100
Countable Groupsp. 105
Quasi-Generic Groupsp. 111
Representations over a Discrete Valuation Ringp. 126
Finite and Rank-Finite Representation Typep. 126
Wild Modulo p Representation Typep. 135
Finite Rank Butler Groups and Isomorphism at pp. 140
Almost Completely Decomposable Groupsp. 144
Characterizations and Propertiesp. 144
Isomorphism at p and Representation Typep. 154
Uniform Groupsp. 164
Primary Regulating Quotient Groupsp. 169
Representations over Fields and Exact Sequencesp. 173
Projectives, Injectives, and Exact Sequencesp. 173
Coxeter Correspondencesp. 178
Almost Split Sequencesp. 187
A Torsion Theory and Localizationsp. 191
Finite Rank Butler Groupsp. 197
Projectives, Injectives, and Exact Sequencesp. 197
Endomorphism Ringsp. 202
Bracket Groupsp. 205
Applications of Representations and Butler Groupsp. 211
Torsion-Free Modules over Discrete Valuation Ringsp. 211
Finite Valuated Groupsp. 218
Referencesp. 223
List of Symbolsp. 235
Index of Termsp. 241
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780387989822
ISBN-10: 038798982X
Series: Cms Advanced Books in Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 244
Published: 16th June 2000
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 22.86 x 15.88  x 1.27
Weight (kg): 0.48

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