Methods of graded rings:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2004
|
| Schriftenreihe: | Lecture notes in mathematics
1836 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 304 S. |
| ISBN: | 3540207465 |
Internformat
MARC
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| 100 | 1 | |a Năstăsescu, Constantin |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Methods of graded rings |c Constantin Nastasescu ; Freddy van Oystaeyen |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2004 | |
| 300 | |a XIII, 304 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 650 | 4 | |a Graded rings | |
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Datensatz im Suchindex
| _version_ | 1804130461883039744 |
|---|---|
| adam_text | Contents
1 The Category of Graded Rings 1
1.1 Graded Rings 1
1.2 The Category of Graded Rings 3
1.3 Examples 4
1.4 Crossed Products 10
1.5 Exercises 13
1.6 Comments and References for Chapter 1 18
2 The Category of Graded Modules 19
2.1 Graded Modules 19
2.2 The category of Graded Modules 20
2.3 Elementary Properties of the Category R gr 22
2.4 The functor H0Mfi( , ) 25
2.5 Some Functorial Constructions 31
2.6 Some Topics in Torsion Theory on R gr 37
2.7 The Structure of Simple Objects in R gr 46
2.8 The Structure of Gr injective Modules 50
2.9 The Graded Jacobson Radical
(Graded Version of Hopkins Theorem) 52
2.10 Graded Endomorphism Rings and Graded Matrix Rings .... 57
2.11 Graded Prime Ideals. The Graded Spectrum 63
2.12 Exercises 70
2.13 Comments and References for Chapter 2 78
3 Modules over Strongly Graded Rings 81
3.1 Dade s Theorem 81
3.2 Graded Rings with R gr Equivalent to R,, mod 83
3.3 Strongly Graded Rings over a Local Ring 85
3.4 Endomorphism G Rings 86
3.5 The Maschke Theorem for Strongly Graded Rings 90
3.6 // regular Modules 94
3.7 Green Theory for Strongly Graded Rings 99
3.8 Exercises 106
3.9 Comments and References for Chapter 3 112
XII CONTENTS
4 Graded Clifford Theory 115
4.1 The Category Mod(_R|E) 115
4.2 The Structure of Objects of Mod(fl|£) as/^ modules 118
4.3 The Classical Clifford Theory for Strongly Graded Rings .... 120
4.4 Application to Graded Clifford Theory 123
4.5 Torsion Theory and Graded Clifford Theory 128
4.6 The Density Theorem for gr simple modules 132
4.7 Extending (Simple) Modules 137
4.8 Exercises 140
4.9 Comments and References for Chapter 4 145
5 Internal Homogenization 147
5.1 Ordered Groups 147
5.2 Gradation by Ordered Groups. Elementary Properties 148
5.3 Internal Homogenization 151
5.4 Chain Conditions for Graded Modules 153
5.5 Krull Dimension of Graded Rings 156
5.6 Exercises 160
5.7 Comments and References for Chapter 5 165
6 External Homogenization 167
6.1 Normal subsemigroup of a group 167
6.2 External homogenization 167
6.3 A Graded Version of Maschke s Theorem. Applications 172
6.4 Homogenization and Dehomogenization Functors 178
6.5 Exercises 181
6.6 Comments and References for Chapter 6 184
7 Smash Products 187
7.1 The Construction of the Smash Product 187
7.2 The Smash Product and the Ring Endfl_gr(C/) 191
7.3 Some Functorial Constructions 194
7.4 Smash Product and Finiteness Conditions 202
7.5 Prime Ideals of Smash Products 208
7.6 Exercises 215
7.7 Comments and References for Chapter 7 220
8 Localization of Graded Rings 223
8.1 Graded rings of fractions 223
8.2 Localization of Graded Rings for a Graded Linear Topology . . 225
8.3 Graded Rings and Modules of Quotients 230
8.4 The Graded Version of Goldie s Theorem 233
8.5 Exercises 236
8.6 Comments and References for Chapter 8 239
CONTENTS XIII
9 Application to Gradability 241
9.1 General Descent Theory 241
9.2 Good gradings on matrix algebras 243
9.3 Gradings over cyclic groups 253
9.4 C2 gradings of A/2(fc) 261
9.5 CVgradings on Ahik) in characteristic 2 269
9.6 Gradability of modules 273
9.7 Comments and References for Chapter 9 276
Appendix A. Some Category Theory 277
Appendix B. Dimensions in an Abelian Category 285
Bibliography 291
Index 303
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:21:24Z |
| institution | BVB |
| isbn | 3540207465 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010663453 |
| oclc_num | 53992845 |
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| physical | XIII, 304 S. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Springer |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Năstăsescu, Constantin Verfasser aut Methods of graded rings Constantin Nastasescu ; Freddy van Oystaeyen Berlin [u.a.] Springer 2004 XIII, 304 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1836 Anneau associatif rasuqam Anneau gradué rasuqam Anneaux associatifs Anneaux gradués Anéis e álgebras associativos larpcal Ringen (wiskunde) gtt Álgebra larpcal Associative rings Graded rings Graduierter Modul (DE-588)4158002-3 gnd rswk-swf Graduierter Ring (DE-588)4158003-5 gnd rswk-swf Graduierter Ring (DE-588)4158003-5 s DE-604 Graduierter Modul (DE-588)4158002-3 s Van Oystaeyen, Freddy 1947- Verfasser (DE-588)128792884 aut Lecture notes in mathematics 1836 (DE-604)BV000676446 1836 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010663453&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Năstăsescu, Constantin Van Oystaeyen, Freddy 1947- Methods of graded rings Lecture notes in mathematics Anneau associatif rasuqam Anneau gradué rasuqam Anneaux associatifs Anneaux gradués Anéis e álgebras associativos larpcal Ringen (wiskunde) gtt Álgebra larpcal Associative rings Graded rings Graduierter Modul (DE-588)4158002-3 gnd Graduierter Ring (DE-588)4158003-5 gnd |
| subject_GND | (DE-588)4158002-3 (DE-588)4158003-5 |
| title | Methods of graded rings |
| title_auth | Methods of graded rings |
| title_exact_search | Methods of graded rings |
| title_full | Methods of graded rings Constantin Nastasescu ; Freddy van Oystaeyen |
| title_fullStr | Methods of graded rings Constantin Nastasescu ; Freddy van Oystaeyen |
| title_full_unstemmed | Methods of graded rings Constantin Nastasescu ; Freddy van Oystaeyen |
| title_short | Methods of graded rings |
| title_sort | methods of graded rings |
| topic | Anneau associatif rasuqam Anneau gradué rasuqam Anneaux associatifs Anneaux gradués Anéis e álgebras associativos larpcal Ringen (wiskunde) gtt Álgebra larpcal Associative rings Graded rings Graduierter Modul (DE-588)4158002-3 gnd Graduierter Ring (DE-588)4158003-5 gnd |
| topic_facet | Anneau associatif Anneau gradué Anneaux associatifs Anneaux gradués Anéis e álgebras associativos Ringen (wiskunde) Álgebra Associative rings Graded rings Graduierter Modul Graduierter Ring |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010663453&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
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