An elementary approach to homological algebra:
"Designed to meet the needs of beginning graduate students, it presents the material in a clear, easy-to-understand manner. Complete, detailed proofs make the material easy to follow, numerous worked examples help readers understand the concepts, and an abundance of exercises test and solidify...
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2003
|
| Series: | Chapman & Hall CRC monographs and surveys in pure and applied mathematics
130 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | "Designed to meet the needs of beginning graduate students, it presents the material in a clear, easy-to-understand manner. Complete, detailed proofs make the material easy to follow, numerous worked examples help readers understand the concepts, and an abundance of exercises test and solidify their understanding."--BOOK JACKET. |
| Item Description: | Includes bibliographical references (S. [309]-312) and index |
| Physical Description: | 315 S. Ill. |
| ISBN: | 1584884002 |
Staff View
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Record in the Search Index
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| adam_text | Titel: An elementary approach to homological algebra
Autor: Vermani, Lekh R
Jahr: 2003
Contents
1 Modules 1
1.1 Modules..........................................................1
1.2 Free Modules....................................................4
1.3 Exact Sequences................................................10
1.4 Homomorphisms................................................18
1.5 Tensor Product of Modules....................................21
1.6 Direct and Inverse Limits......................................28
1.7 Pull Back and Push Out........................................85
2 Categories and Functors 41
2.1 Categories........................................................41
2.2 Functors..........................................................54
2.3 The Functors Horn and Tensor................................63
3 Projective and Injective Modules 73
3.1 Projective Modules..............................................73
3.2 Injective Modules................................................80
3.3 Baer s Criterion..................................................83
3.4 An Embedding Theorem........................................88
4 Homology of Complexes 97
4.1 Ker - Coker Sequence..........................................97
4.2 Connecting Homomorphism - the General Case.......105
4.3 Homotopy........................................................H2
5 Derived Functors 117
5.1 Projective Resolutions..........................................117
5.2 Injective Resolutions............................................122
5.3 Derived Functors................................................125
6 Torsion and Extension Functors 145
6.1 Derived Functors - Revisited..................................145
6.2 Torsion and Extension Functors................................147
6.3 Some Further Properties of Tor%..............................155
CONTENTS
6.4 Tor and Direct Limits..........................................^
7 The Functor Ext^
7.1 Ext1 and Extensions............................................*67
7.2 Baer Sum of Extensions........................................178
7.3 Some Further Properties of ExTr...............184
8 Hereditary and Semihereditary Rings 189
8.1 Hereditary Rings and Dedekind Domains ....................189
8.2 Invertible Ideals and Dedekind Rings..........................196
8.3 Semihereditary and Priifer Rings...............200
9 Universal Coefficient Theorem 203
9.1 Universal Coefficient Theorem for Homology.........203
9.2 Universal Coefficient Theorem for Cohomology.......206
9.3 The Kunneth Formula - A Special Case...........209
10 Dimensions of Modules and Rings 215
10.1 Projectively and Injectively Equivalent Modules.......215
10.2 Dimensions of Modules and Rings ..............220
10.3 Global Dimension of Rings ..................224
10.4 Global Dimension of Noetherian Rings............227
10.5 Global Dimension of Artin Rings...............234
11 Cohomology of Groups 239
11.1 Homology and Cohomology Groups..............239
11.2 Some Examples.........................242
11.3 The Groups H°(G, A) and Ho(G, A).............245
11.4 The Groups Hl {G, A) and Hi (G, A).............246
11.5 Homology and Cohomology of Direct Sums.........250
11.6 The Bar Resolution.......................256
11.7 Second Cohomology Group and Extensions.........262
11.8 Some Homomorphisms.....................267
11.9 Some Exact Sequences.....................278
12 Some Applications 293
12.1 An Exact Sequence..............................................293
12.2 Outer Automorphisms of p-Groups..............298
12.3 A Theorem of Magnus.....................303
Bibliography 30g
Index
313
|
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| indexdate | 2024-07-09T19:13:03Z |
| institution | BVB |
| isbn | 1584884002 |
| language | English |
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| series | Chapman & Hall CRC monographs and surveys in pure and applied mathematics |
| series2 | Chapman & Hall CRC monographs and surveys in pure and applied mathematics |
| spelling | Vermani, Lekh R. Verfasser (DE-588)172906113 aut An elementary approach to homological algebra L. R. Vermani Boca Raton [u.a.] Chapman & Hall/CRC 2003 315 S. Ill. txt rdacontent n rdamedia nc rdacarrier Chapman & Hall CRC monographs and surveys in pure and applied mathematics 130 Includes bibliographical references (S. [309]-312) and index "Designed to meet the needs of beginning graduate students, it presents the material in a clear, easy-to-understand manner. Complete, detailed proofs make the material easy to follow, numerous worked examples help readers understand the concepts, and an abundance of exercises test and solidify their understanding."--BOOK JACKET. Álgebra homológica larpcal Algebra, Homological Homologische Algebra (DE-588)4160598-6 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Homologische Algebra (DE-588)4160598-6 s DE-604 Chapman & Hall CRC monographs and surveys in pure and applied mathematics 130 (DE-604)BV013350872 130 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010282399&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Vermani, Lekh R. An elementary approach to homological algebra Chapman & Hall CRC monographs and surveys in pure and applied mathematics Álgebra homológica larpcal Algebra, Homological Homologische Algebra (DE-588)4160598-6 gnd |
| subject_GND | (DE-588)4160598-6 (DE-588)4151278-9 |
| title | An elementary approach to homological algebra |
| title_auth | An elementary approach to homological algebra |
| title_exact_search | An elementary approach to homological algebra |
| title_full | An elementary approach to homological algebra L. R. Vermani |
| title_fullStr | An elementary approach to homological algebra L. R. Vermani |
| title_full_unstemmed | An elementary approach to homological algebra L. R. Vermani |
| title_short | An elementary approach to homological algebra |
| title_sort | an elementary approach to homological algebra |
| topic | Álgebra homológica larpcal Algebra, Homological Homologische Algebra (DE-588)4160598-6 gnd |
| topic_facet | Álgebra homológica Algebra, Homological Homologische Algebra Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010282399&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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