Injective objects in categories of unstable K-modules:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Bonn
1999
|
| Schriftenreihe: | Bonner mathematische Schriften
316 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IV, 130 S. |
Internformat
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| 100 | 1 | |a Meyer, Dagmar M. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Injective objects in categories of unstable K-modules |c Dagmar M. Meyer |
| 264 | 1 | |a Bonn |c 1999 | |
| 300 | |a IV, 130 S. | ||
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| 490 | 1 | |a Bonner mathematische Schriften |v 316 | |
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| 650 | 4 | |a Injective modules (Algebra) | |
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Datensatz im Suchindex
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| adam_text | Contents
List of frequently used notation i
1 Introduction and statement of results 1
1.1 Historical background 1
1.2 Statement of results 4
1.3 Acknowledgements 7
2 Background material on categories of unstable modules and algebras 8
2.1 Basic definitions and notation 8
2.2 A Morita theorem for K U 11
2.3 The functors E and O 12
2.4 Nilpotent and reduced modules 14
2.5 Free modules and Brown Gitler modules in K — U 16
3 Lannes T functor and special injectives in K U 23
3.1 Review of the T functor definitions and properties 23
3.2 The functors Fix ^Wy) 29
3.3 A generalized linearization principle 31
3.4 A generalized splitting theorem 33
3.5 Some special injectives in if — U 40
4 The categories S{K), Tl(K) and T(y) and some of their properties 47
4.1 The categories S(K) and K{K) and invariant prime ideals in if 47
4.2 A description of morphisms in S(K) by matrices 50
4.3 The category F(y) and generalized polynomial functors 53
5 Locally noetherian categories 60
5.1 Some category theoretical background material 60
5.2 K — U is locally noetherian if if is noetherian 65
iii
6 Proof of the classification theorems for K U and Kjg U 68
6.1 The indecomposability of Ek{u) 8
6.1.1 The case n = 0 69
6.1.2 The case n 0 72
6.2 The uniqueness of the parameters w 6 CIk 72
6.3 The completeness of {ek(u)}u 1k 73
6.3.1 The torsion free case 74
6.3.2 The general case 7f*
6.4 A simpler description of Ek{u) 81
6.4.1 The functors r^^ 81
6.4.2 The alternative description of Ek(u) in the general case 82
6.5 The classification theorem for Kjg U 84
7 Applications 85
7.1 A simple proof of Prop. 2.2 in [LZ3] 85
7.2 Localizations in K U away from torsion modules 86
8 Some examples 99
8.1 Example: K = H*(D2™;F2) 100
8.2 Example: K = H* (Q2™; F2) 106
8.3 Example: K = ff*(S4;F2) 107
8.4 Example: K = D(m,s) 110
A Review of some algebraic facts and definitions 117
B Proof of Theorem 5.2.1 123
Bibliography 126
iv
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| indexdate | 2024-07-09T18:28:19Z |
| institution | BVB |
| language | English |
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| physical | IV, 130 S. |
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| series | Bonner mathematische Schriften |
| series2 | Bonner mathematische Schriften |
| spelling | Meyer, Dagmar M. Verfasser aut Injective objects in categories of unstable K-modules Dagmar M. Meyer Bonn 1999 IV, 130 S. txt rdacontent n rdamedia nc rdacarrier Bonner mathematische Schriften 316 Heidelberg, Univ., Diss., 1998 Categories (Mathematics) Injective modules (Algebra) K-theory Injektiver Modul (DE-588)4161753-8 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Injektiver Modul (DE-588)4161753-8 s DE-604 Bonner mathematische Schriften 316 (DE-604)BV000001610 316 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008470365&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Meyer, Dagmar M. Injective objects in categories of unstable K-modules Bonner mathematische Schriften Categories (Mathematics) Injective modules (Algebra) K-theory Injektiver Modul (DE-588)4161753-8 gnd |
| subject_GND | (DE-588)4161753-8 (DE-588)4113937-9 |
| title | Injective objects in categories of unstable K-modules |
| title_auth | Injective objects in categories of unstable K-modules |
| title_exact_search | Injective objects in categories of unstable K-modules |
| title_full | Injective objects in categories of unstable K-modules Dagmar M. Meyer |
| title_fullStr | Injective objects in categories of unstable K-modules Dagmar M. Meyer |
| title_full_unstemmed | Injective objects in categories of unstable K-modules Dagmar M. Meyer |
| title_short | Injective objects in categories of unstable K-modules |
| title_sort | injective objects in categories of unstable k modules |
| topic | Categories (Mathematics) Injective modules (Algebra) K-theory Injektiver Modul (DE-588)4161753-8 gnd |
| topic_facet | Categories (Mathematics) Injective modules (Algebra) K-theory Injektiver Modul Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008470365&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001610 |
| work_keys_str_mv | AT meyerdagmarm injectiveobjectsincategoriesofunstablekmodules |