Author | Arnold, David M. author |
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Title | Abelian Groups and Representations of Finite Partially Ordered Sets [electronic resource] / by David M. Arnold |
Imprint | New York, NY : Springer New York : Imprint: Springer, 2000 |
Connect to | http://dx.doi.org/10.1007/978-1-4419-8750-1 |
Descript | XII, 244 p. online resource |
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