Model theory and modules:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge u.a.
Cambridge Univ. Pr.
1988
|
| Edition: | 1. publ. |
| Series: | London Mathematical Society: London Mathematical Society lecture note series
130. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 351 - 369 |
| Physical Description: | XVIII, 380 S. |
| ISBN: | 0521348331 |
Staff View
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| 100 | 1 | |a Prest, Mike |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Model theory and modules |
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| 490 | 1 | |a London Mathematical Society: London Mathematical Society lecture note series |v 130. | |
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Record in the Search Index
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| adam_text | Contents
Introduction xi
Acknowledgements xi
Notations and conventions xii
Remarks on the development of the area xiii
Section summaries xv
Chapter 1 Some preliminaries 1
1.1 An introduction to model theory 1
1.2 Injective modules and decomposition theorems 8
Chapter 2 Positive primitive formulas and the sets they define 13
2.2 pp formulas 14
2.2 pp types 22
2.3 Pure embeddings and pure injective modules 27
2.4 pp elimination of quantifiers 32
2.5 Immediate corollaries of pp elimination of quantifiers 39
2.6 Comparison of complete theories of modules 41
2.2 pp formulas and types in abelian groups 44
2.L Other languages 52
Chapter 3 Stability and totally transcendental modules 54
3.1 Stability for modules 55
3.2 A structure theorem for totally transcendental modules; part I 60
3.A Abelian structures 63
Chapter 4 Hulls 67
4.1 pp essential embeddings and the construction of hulls 68
4.2 Examples of hulls 76
4.3 Decomposition of injective and pure injective modules 80
4.4 Irreducible types 83
4.5 Limited and unlimited types 89
4.6 A structure theory for totally transcendental modules; part II 91
4.C Categoricity 100
4.7 The space of indecomposables 102
Chapter 5 Forking and ranks 109
5.1 Forking and independence 109
5.2 Ranks 116
5.3 An algebraic characterisation of independence 123
5.4 Independence when T = T^*« 125
Chapter 6 Stability theoretic properties of types 132
6.1 Free parts of types and the stratified order 132
6.2 Domination and the RK order 136
6.3 Orthogonality and the RK order 141
6.4 Regular types 143
6.1 An example: injective modules over noetherian rings 149
6.5 Saturation and pure injective modules 150
6.6 Multiplicity and strong types 152
Chapter 7 Superstable modules 155
7.1 Superstable modules: the uncountable spectrum 155
7.2 Modules of U rank 1 157
7.3 Modules of finite U rank 171
Chapter 8 The lattice of pp types and free realisations of pp types 173
8.1 The lattice of pp types 173
8.2 Finitely generated pp types 176
8.3 pp types and matrices 178
8.3 Duality and pure semisimple rings 184
Chapter 9 Types and the structure of pure injective modules 188
9.1 Minimal pairs 188
9.2 Associated types 191
9.3 Notions of isolation 194
9.4 Neg isolated types and elementary cogenerators 198
Chapter 10 Dimension and decomposition 201
10.1 Existence of indecomposable direct summands 202
10.2 Dimensions defined on lattices 203
10.3 Modules with width 208
10.4 Classification for theories with dimension 211
10.5 Krull dimension 216
10.T Te°. 220
10.6 Dimension and height 222
10.V Valuation rings 225
Chapter 11 Modules over artinian rings 228
11.1 Pure semisimple rings 228
11.2 Pure semisimple rings and rings of finite representation type 233
11.3 Finite hulls over artinian rings 237
11.4 Finite Morley rank and finite representation type 241
11.P Pathologies 245
Chapter 12 Functor categories 247
12.1 Functors defined from pp formulas 248
12.2 Simple functors 254
12.3 Embedding into functor categories 258
12.P Pure global dimension and dimensions of functor categories 265
Chapter 13 Modules over Artin algebras 267
13.1 The space of indecomposables 267
13.2 Representation type of quivers 270
13.3 Describing the space of indecomposables 277
Chapter 14 Projective and flat modules 283
14.1 Definable subgroups of flat and projective modules 283
14.2 Projective modules and totally transcendental rings 289
Chapter 15 Torsion and torsionfree classes 294
15.1 Torsion, torsionfree classes and radicals 294
15.2 Universal Horn classes, varieties and torsion classes 298
15.3 Model companions and model completions of universal Horn classes 301
15.4 Elementary localisation 313
Chapter 16 Elimination of quantifiers 317
16.1 Complete elimination of quantifiers and its consequences 317
16.2 Modules over regular rings 323
16.C Continuous pure injectives 330
Chapter 17 Decidability and undecidability 332
17.1 Introduction 332
17.2 Undecidability 337
17.3 Decidability 342
17.4 Summary 348
Problems page 350
Bibliography 351
Examples index 370
Notation index 371
Index 373
|
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| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV006559211 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:48:18Z |
| institution | BVB |
| isbn | 0521348331 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004183056 |
| oclc_num | 246643894 |
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| physical | XVIII, 380 S. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | Cambridge Univ. Pr. |
| record_format | marc |
| series | London Mathematical Society: London Mathematical Society lecture note series |
| series2 | London Mathematical Society: London Mathematical Society lecture note series |
| spelling | Prest, Mike Verfasser aut Model theory and modules 1. publ. Cambridge u.a. Cambridge Univ. Pr. 1988 XVIII, 380 S. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society: London Mathematical Society lecture note series 130. Literaturverz. S. 351 - 369 Modul (DE-588)4129770-2 gnd rswk-swf Modelltheorie (DE-588)4114617-7 gnd rswk-swf Modelltheorie (DE-588)4114617-7 s Modul (DE-588)4129770-2 s DE-604 London Mathematical Society: London Mathematical Society lecture note series 130. (DE-604)BV000000130 130 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004183056&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Prest, Mike Model theory and modules London Mathematical Society: London Mathematical Society lecture note series Modul (DE-588)4129770-2 gnd Modelltheorie (DE-588)4114617-7 gnd |
| subject_GND | (DE-588)4129770-2 (DE-588)4114617-7 |
| title | Model theory and modules |
| title_auth | Model theory and modules |
| title_exact_search | Model theory and modules |
| title_full | Model theory and modules |
| title_fullStr | Model theory and modules |
| title_full_unstemmed | Model theory and modules |
| title_short | Model theory and modules |
| title_sort | model theory and modules |
| topic | Modul (DE-588)4129770-2 gnd Modelltheorie (DE-588)4114617-7 gnd |
| topic_facet | Modul Modelltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004183056&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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