An introduction to homological algebra:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer
2009
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 709 S. graph. Darst. |
| ISBN: | 0387245278 9780387245270 |
Internformat
MARC
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| 100 | 1 | |a Rotman, Joseph J. |d 1934- |e Verfasser |0 (DE-588)120676826 |4 aut | |
| 245 | 1 | 0 | |a An introduction to homological algebra |c Joseph J. Rotman |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York, NY |b Springer |c 2009 | |
| 300 | |a XIV, 709 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Universitext | |
| 650 | 4 | |a Algèbre homologique | |
| 650 | 4 | |a Algebra, Homological | |
| 650 | 0 | 7 | |a Homologische Algebra |0 (DE-588)4160598-6 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4151278-9 |a Einführung |2 gnd-content | |
| 689 | 0 | 0 | |a Homologische Algebra |0 (DE-588)4160598-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-0-387-68324-9 |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-016260881 | ||
Datensatz im Suchindex
| _version_ | 1804137293372456960 |
|---|---|
| adam_text | Contents
Preface
to the Second Edition
...................
x
How to Read This Book
.......................xiii
Chapter
1
Introduction
1.1
Simplicial Homology
...................... 1
1.2
Categories and Functors
..................... 7
1.3
Singular Homology
.......................29
Chapter
2
Hom
and Tensor
2.1
Modules
.............................37
2.2
Tensor Products
.........................69
2.2.1
Adjoint Isomorphisms
......................91
Chapter
3
Special Modules
3.1
Projective
Modules
....................... 98
3.2
Injective Modules
........................ 115
3.3
Flat Modules
.......................... 131
3.3.1
Purity
.............................. 146
Chapter
4
Specific Rings
4.1 Semisimple
Rings
........................154
4.2 von
Neumann Regular Rings
..................159
4.3
Hereditary and Dedekind Rings
.................160
viii
Contents
4.4 Semihereditary and Prüfer
Rings
................169
4.5
Quasi-Frobenius Rings
.....................173
4.6
Semiperfect Rings
........................179
4.7
Localization
...........................188
4.8
Polynomial Rings
........................203
Chapter
5
Setting the Stage
5.1
Categorical Constructions
....................213
5.2
Limits
..............................229
5.3
Adjoint Functor Theorem for Modules
.............256
5.4
Sheaves
.............................273
5.4.1
Manifolds
............................288
5.4.2
Sheaf Constructions
.......................294
5.5
Abelian Categories
.......................303
5.5.1
Complexes
............................317
Chapter
6
Homology
6.1
Homology Functors
.......................323
6.2
Derived Functors
........................340
6.2.1
Left Derived Functors
......................343
6.2.2
Axioms
.............................357
6.2.3
Covariant Right Derived Functors
...............364
6.2.4
Contravariant
Right Derived Functors
.............369
6.3
Sheaf Cohomology
.......................377
6.3.1
Čech
Cohomology
.......................384
6.3.2
Riemann-Roch Theorem
....................392
Chapter
7
Tor and Ext
7.1
Tor
................................404
7.1.1
Domains
.............................412
7.1.2
Localization
...........................415
7.2
Ext
................................418
7.2.1
BaerSum
............................428
7.3
Cotorsion Groups
........................438
7.4
Universal Coefficients
......................448
Chapter
8
Homology and Rings
8.1
Dimensions of Rings
......................453
8.2
Hubert s Syzygy Theorem
...................467
8.3
Stably Free Modules
......................476
8.4
Commutative Noetherian Local Rings
.............484
Contents
ix
Chapter
9
Homology and Groups
9.1
Group Extensions
........................495
9.1.1
Semidirect Products
.......................500
9.1.2
General Extensions and Cohomology
..............504
9.1.3
Stabilizing Automorphisms
...................514
9.2
Group Cohomology
.......................519
9.3
Bar Resolutions
.........................525
9.4
Group Homology
........................535
9.4.1 Schur
Multiplier
.........................541
9.5
Change of Groups
........................559
9.5.1
Restriction and Inflation
.....................564
9.6
Transfer
.............................572
9.7
Tate
Groups
...........................580
9.8
Outer Automorphisms of p-Groups
...............587
9.9
Cohomological Dimension
...................591
9.10
Division Rings and
Brauer
Groups
...............595
Chapter
10
Spectral Sequences
10.1
Bicomplexes
...........................609
10.2
Filtrations and Exact Couples
..................616
10.3
Convergence
...........................624
10.4
Homology of the Total Complex
................628
10.5
Cartan-Eilenberg Resolutions
.................647
10.6
Grothendieck Spectral Sequences
................656
10.7
Groups
..............................660
10.8
Rings
..............................666
10.9
Sheaves
.............................675
10.10 Künneth
Theorems
.......................678
References
...............................689
Special Notation
............................695
Index
...................................697
|
| adam_txt |
Contents
Preface
to the Second Edition
.
x
How to Read This Book
.xiii
Chapter
1
Introduction
1.1
Simplicial Homology
. 1
1.2
Categories and Functors
. 7
1.3
Singular Homology
.29
Chapter
2
Hom
and Tensor
2.1
Modules
.37
2.2
Tensor Products
.69
2.2.1
Adjoint Isomorphisms
.91
Chapter
3
Special Modules
3.1
Projective
Modules
. 98
3.2
Injective Modules
. 115
3.3
Flat Modules
. 131
3.3.1
Purity
. 146
Chapter
4
Specific Rings
4.1 Semisimple
Rings
.154
4.2 von
Neumann Regular Rings
.159
4.3
Hereditary and Dedekind Rings
.160
viii
Contents
4.4 Semihereditary and Prüfer
Rings
.169
4.5
Quasi-Frobenius Rings
.173
4.6
Semiperfect Rings
.179
4.7
Localization
.188
4.8
Polynomial Rings
.203
Chapter
5
Setting the Stage
5.1
Categorical Constructions
.213
5.2
Limits
.229
5.3
Adjoint Functor Theorem for Modules
.256
5.4
Sheaves
.273
5.4.1
Manifolds
.288
5.4.2
Sheaf Constructions
.294
5.5
Abelian Categories
.303
5.5.1
Complexes
.317
Chapter
6
Homology
6.1
Homology Functors
.323
6.2
Derived Functors
.340
6.2.1
Left Derived Functors
.343
6.2.2
Axioms
.357
6.2.3
Covariant Right Derived Functors
.364
6.2.4
Contravariant
Right Derived Functors
.369
6.3
Sheaf Cohomology
.377
6.3.1
Čech
Cohomology
.384
6.3.2
Riemann-Roch Theorem
.392
Chapter
7
Tor and Ext
7.1
Tor
.404
7.1.1
Domains
.412
7.1.2
Localization
.415
7.2
Ext
.418
7.2.1
BaerSum
.428
7.3
Cotorsion Groups
.438
7.4
Universal Coefficients
.448
Chapter
8
Homology and Rings
8.1
Dimensions of Rings
.453
8.2
Hubert's Syzygy Theorem
.467
8.3
Stably Free Modules
.476
8.4
Commutative Noetherian Local Rings
.484
Contents
ix
Chapter
9
Homology and Groups
9.1
Group Extensions
.495
9.1.1
Semidirect Products
.500
9.1.2
General Extensions and Cohomology
.504
9.1.3
Stabilizing Automorphisms
.514
9.2
Group Cohomology
.519
9.3
Bar Resolutions
.525
9.4
Group Homology
.535
9.4.1 Schur
Multiplier
.541
9.5
Change of Groups
.559
9.5.1
Restriction and Inflation
.564
9.6
Transfer
.572
9.7
Tate
Groups
.580
9.8
Outer Automorphisms of p-Groups
.587
9.9
Cohomological Dimension
.591
9.10
Division Rings and
Brauer
Groups
.595
Chapter
10
Spectral Sequences
10.1
Bicomplexes
.609
10.2
Filtrations and Exact Couples
.616
10.3
Convergence
.624
10.4
Homology of the Total Complex
.628
10.5
Cartan-Eilenberg Resolutions
.647
10.6
Grothendieck Spectral Sequences
.656
10.7
Groups
.660
10.8
Rings
.666
10.9
Sheaves
.675
10.10 Künneth
Theorems
.678
References
.689
Special Notation
.695
Index
.697 |
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| author | Rotman, Joseph J. 1934- |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 320 |
| ctrlnum | (OCoLC)263935394 (DE-599)GBV477550118 |
| dewey-full | 512/.64 512/.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.64 512/.55 |
| dewey-search | 512/.64 512/.55 |
| dewey-sort | 3512 264 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2. ed. |
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| genre | (DE-588)4151278-9 Einführung gnd-content |
| genre_facet | Einführung |
| id | DE-604.BV023057614 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:27:24Z |
| indexdate | 2024-07-09T21:09:59Z |
| institution | BVB |
| isbn | 0387245278 9780387245270 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016260881 |
| oclc_num | 263935394 |
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| physical | XIV, 709 S. graph. Darst. |
| publishDate | 2009 |
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| publishDateSort | 2009 |
| publisher | Springer |
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| series2 | Universitext |
| spelling | Rotman, Joseph J. 1934- Verfasser (DE-588)120676826 aut An introduction to homological algebra Joseph J. Rotman 2. ed. New York, NY Springer 2009 XIV, 709 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Algèbre homologique 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 Erscheint auch als Online-Ausgabe 978-0-387-68324-9 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016260881&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rotman, Joseph J. 1934- An introduction to homological algebra Algèbre homologique Algebra, Homological Homologische Algebra (DE-588)4160598-6 gnd |
| subject_GND | (DE-588)4160598-6 (DE-588)4151278-9 |
| title | An introduction to homological algebra |
| title_auth | An introduction to homological algebra |
| title_exact_search | An introduction to homological algebra |
| title_exact_search_txtP | An introduction to homological algebra |
| title_full | An introduction to homological algebra Joseph J. Rotman |
| title_fullStr | An introduction to homological algebra Joseph J. Rotman |
| title_full_unstemmed | An introduction to homological algebra Joseph J. Rotman |
| title_short | An introduction to homological algebra |
| title_sort | an introduction to homological algebra |
| topic | Algèbre homologique Algebra, Homological Homologische Algebra (DE-588)4160598-6 gnd |
| topic_facet | Algèbre homologique Algebra, Homological Homologische Algebra Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016260881&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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