CMS Books in Mathematics

By: David Arnold

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Hardcover | 1 July 2000

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Hardcover
260 Pages

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22.86 x 15.88 x 1.27

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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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MATHEMATICAL REVIEWS

"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."

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Non-Fiction Mathematics Algebra Groups & Group Theory

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Paperback

Published: 24th October 2012

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Preface
Representations of Posets over a Field	p. 1
Vector Spaces with Distinguished Subspaces	p. 1
Representations of Posets and Matrix Problems	p. 10
Finite Representation Type	p. 19
Tame and Wild Representation Type	p. 31
Generic Representations	p. 39
Torsion-Free Abelian Groups	p. 47
Quasi-isomorphism and Isomorphism at p	p. 47
Near-isomorphism of Finite Rank Groups	p. 56
Stable Range Conditions for Finite Rank Groups	p. 62
Self-Small Groups and Endomorphism Rings	p. 69
Butler Groups	p. 76
Types and Completely Decomposable Groups	p. 76
Characterizations of Finite Rank Groups	p. 88
Quasi-isomorphism and Q-Representations of Posets	p. 100
Countable Groups	p. 105
Quasi-Generic Groups	p. 111
Representations over a Discrete Valuation Ring	p. 126
Finite and Rank-Finite Representation Type	p. 126
Wild Modulo p Representation Type	p. 135
Finite Rank Butler Groups and Isomorphism at p	p. 140
Almost Completely Decomposable Groups	p. 144
Characterizations and Properties	p. 144
Isomorphism at p and Representation Type	p. 154
Uniform Groups	p. 164
Primary Regulating Quotient Groups	p. 169
Representations over Fields and Exact Sequences	p. 173
Projectives, Injectives, and Exact Sequences	p. 173
Coxeter Correspondences	p. 178
Almost Split Sequences	p. 187
A Torsion Theory and Localizations	p. 191
Finite Rank Butler Groups	p. 197
Projectives, Injectives, and Exact Sequences	p. 197
Endomorphism Rings	p. 202
Bracket Groups	p. 205
Applications of Representations and Butler Groups	p. 211
Torsion-Free Modules over Discrete Valuation Rings	p. 211
Finite Valuated Groups	p. 218
References	p. 223
List of Symbols	p. 235
Index of Terms	p. 241
Table of Contents provided by Blackwell. All Rights Reserved.

CMS Books in Mathematics

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