Table of contents for Abelian groups and representations of finite partially ordered sets / David M. Arnold.

Contents

Preface                                                     vii
1    Representations of Posets over a Field                   1
       
     1.1 Vector Spaces with Distinguished Subspaces ......    1 
     1.2 Representations of Posets and Matrix Problems ...   10 
     1.3 Finite Representation Type ......................   19 
     1.4 Tame and Wild Representation Type ...............   31 
     1.5 Generic Representations .........................   39

2    Torsion-Free Abelian Groups                             47
     2.1 Quasi-isomorphism and Isomorphism at p ..........   47 
     2.2 Near-isomorphism of Finite Rank Groups ..........   56 
     2.3 Stable Range Conditions for Finite Rank Groups ..   62 
     2.4 Self-Small Groups and Endomorphism Rings ........   69

3    Butler Groups                                           76
     3.1 Types and Completely Decomposable Groups ........   76 
     3.2 Characterizations of Finite Rank Groups .........   88 
     3.3 Quasi-isomorphism and Q-Representations of Posets  100 
     3.4 Countable Groups ................................  105 
     3.5 Quasi-Generic Groups ............................  111 

4    Representations over a Discrete Valuation Ring         126
     4.1 Finite and Rank-Finite Representation Type ......  126 
     4.2 Wild Modulo p Representation Type ...............  135 
     4.3 Finite Rank Butler Groups and Isomorphism at p ..  140 

5    Almost Completely Decomposable Groups                  144
     5.1 Characterizations and Properties ................  144 
     5.2 Isomorphism at p and Representation Type ........  154 
     5.3 Uniform Groups ..................................  164 
     5.4 Primary Regulating Quotient Groups ..............  169 

6    Representations over Fields and Exact Sequences        173
     6.1 Projectives, Injectives, and Exact Sequences ....  173 
     6.2 Coxeter Correspondences .........................  178 
     6.3 Almost Split Sequences ..........................  187 
     6.4 A Torsion Theory and Localizations ..............  191 

7    Finite Rank Butler Groups                              197 
     7.1 Projectives, Injectives, and Exact Sequences ....  197 
     7.2 Endomorphism Rings ..............................  202 
     7.3 Bracket Groups ..................................  205 



                                                            8   
Applications of Representations and Butler Groups           211 
     8.1 Torsion-Free Modules over Discrete Valuation
     Rings ...............................................  211
     8.2 Finite Valuated Groups ..........................  218

References                                                  223
List of Symbols                                             235
Index of Terms                                              241