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Abelian Groups and Representations of Finite Partially Ordered Sets David Arnold

Abelian Groups and Representations of Finite Partially Ordered Sets By David Arnold

Abelian Groups and Representations of Finite Partially Ordered Sets by David Arnold

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Summary

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.

Abelian Groups and Representations of Finite Partially Ordered Sets Summary

Abelian Groups and Representations of Finite Partially Ordered Sets by David Arnold

The theme of this book is 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.

Abelian Groups and Representations of Finite Partially Ordered Sets Reviews

From the reviews:

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.

Table of 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.

Additional information

NPB9780387989822
9780387989822
038798982X
Abelian Groups and Representations of Finite Partially Ordered Sets by David Arnold
David Arnold
CMS Books in Mathematics
New
Hardback
Springer-Verlag New York Inc.
2000-06-16
244
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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Customer Reviews - Abelian Groups and Representations of Finite Partially Ordered Sets