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Abelian Groups and Representations of Finite Partially Ordered Sets [Hardcover]

David Arnold

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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.

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