Basic homological algebra:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2000
|
| Series: | Graduate texts in mathematics
196 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 383 - 387 |
| Physical Description: | X, 395 S. graph. Darst. : 24 cm |
| ISBN: | 038798934X |
Staff View
MARC
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| 100 | 1 | |a Osborne, M. Scott |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Basic homological algebra |c M. Scott Osborne |
| 264 | 1 | |a New York [u.a.] |b Springer |c 2000 | |
| 300 | |a X, 395 S. |b graph. Darst. : 24 cm | ||
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| 490 | 1 | |a Graduate texts in mathematics |v 196 | |
| 500 | |a Literaturverz. S. 383 - 387 | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface v
1 Categories 1
2 Modules 11
2.1 Generalities 11
2.2 Tensor Products 14
2.3 Exactness of Functors 22
2.4 Projectives, Injectives, and Flats 28
3 Ext and Tor 39
3.1 Complexes and Projective Resolutions 39
3.2 Long Exact Sequences 47
3.3 Flat Resolutions and Injective Resolutions 55
3.4 Consequences 66
4 Dimension Theory 73
4.1 Dimension Shifting 73
4.2 When Flats are Projective 79
4.3 Dimension Zero 82
4.4 An Example 91
5 Change of Rings 99
5.1 Computational Considerations 99
5.2 Matrix Rings 104
5.3 Polynomials 106
5.4 Quotients and Localization 110
6 Derived Functors 123
6.1 Additive Functors 123
6.2 Derived Functors 126
x Contents
6.3 Long Exact Sequences—I. Existence 130
6.4 Long Exact Sequences—II. Naturality 140
6.5 Long Exact Sequences—III. Weirdness 147
6.6 Universality of Ext 151
7 Abstract Homological Algebra 165
7.1 Living Without Elements 165
7.2 Additive Categories 169
7.3 Kernels and Cokernels 173
7.4 Cheating with Projectives 186
7.5 (Interlude) Arrow Categories 202
7.6 Homology in Abelian Categories 213
7.7 Long Exact Sequences 225
7.8 An Alternative for Unbalanced Categories 239
8 Colimits and Tor 257
8.1 Limits and Colimits 257
8.2 Adjoint Functors 264
8.3 Directed Colimits, ®, and Tor 270
8.4 Lazard s Theorem 274
8.5 Weak Dimension Revisited 280
9 Odds and Ends 285
9.1 Injective Envelopes 285
9.2 Universal Coefficients 290
9.3 The Kunneth Theorems 296
9.4 Do Connecting Homomorphisms Commute? 309
9.5 The Ext Product 318
9.6 The Jacobson Radical, Nakayama s Lemma, and Quasilocal
Rings 324
9.7 Local Rings and Localization Revisited (Expository) .... 331
A GCDs, LCMs, PIDs, and UFDs 337
B The Ring of Entire Functions 345
C The Mitchell Freyd Theorem and Cheating in Abelian Cat¬
egories 359
D Noether Correspondences in Abelian Categories 363
Solution Outlines 373
References 383
Symbol Index 389
Index 391
|
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| dewey-tens | 510 - Mathematics |
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| indexdate | 2024-07-09T18:43:14Z |
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| isbn | 038798934X |
| language | English |
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| physical | X, 395 S. graph. Darst. : 24 cm |
| publishDate | 2000 |
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| publisher | Springer |
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| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Osborne, M. Scott Verfasser aut Basic homological algebra M. Scott Osborne New York [u.a.] Springer 2000 X, 395 S. graph. Darst. : 24 cm txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 196 Literaturverz. S. 383 - 387 Algèbre homologique Algèbre homologique ram Homologische algebra gtt algèbre homologique inriac topologie algébrique inriac Algebra, Homological Homologische Algebra (DE-588)4160598-6 gnd rswk-swf Homologische Algebra (DE-588)4160598-6 s DE-604 Graduate texts in mathematics 196 (DE-604)BV000000067 196 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009061720&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Osborne, M. Scott Basic homological algebra Graduate texts in mathematics Algèbre homologique Algèbre homologique ram Homologische algebra gtt algèbre homologique inriac topologie algébrique inriac Algebra, Homological Homologische Algebra (DE-588)4160598-6 gnd |
| subject_GND | (DE-588)4160598-6 |
| title | Basic homological algebra |
| title_auth | Basic homological algebra |
| title_exact_search | Basic homological algebra |
| title_full | Basic homological algebra M. Scott Osborne |
| title_fullStr | Basic homological algebra M. Scott Osborne |
| title_full_unstemmed | Basic homological algebra M. Scott Osborne |
| title_short | Basic homological algebra |
| title_sort | basic homological algebra |
| topic | Algèbre homologique Algèbre homologique ram Homologische algebra gtt algèbre homologique inriac topologie algébrique inriac Algebra, Homological Homologische Algebra (DE-588)4160598-6 gnd |
| topic_facet | Algèbre homologique Homologische algebra algèbre homologique topologie algébrique Algebra, Homological Homologische Algebra |
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