A course in homological algebra:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
1997
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Graduate texts in mathematics
4 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 364 S. |
| ISBN: | 0387948236 |
Internformat
MARC
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| 100 | 1 | |a Hilton, Peter John |d 1923-2010 |e Verfasser |0 (DE-588)115702822 |4 aut | |
| 245 | 1 | 0 | |a A course in homological algebra |c P. J. Hilton ; U. Stammbach |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 1997 | |
| 300 | |a XII, 364 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate texts in mathematics |v 4 | |
| 650 | 0 | 7 | |a Homologische Algebra |0 (DE-588)4160598-6 |2 gnd |9 rswk-swf |
| 655 | 7 | |8 1\p |0 (DE-588)4151278-9 |a Einführung |2 gnd-content | |
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Datensatz im Suchindex
| _version_ | 1804125721585516544 |
|---|---|
| adam_text | Contents
Preface
to the Second Edition
vn
Introduction
......................
j
I. Modules
....................... 10
1.
Modules
.....................
И
2.
The Group of Homomorphisms
........... 16
3.
Sums and Products
................ 18
4.
Free and
Projective
Modules
............ 22
5.
Projective
Modules over a Principal Ideal Domain
... 26
6.
Dualization, Injective Modules
........... 28
7.
Injective Modules over a Principal Ideal Domain
... 31
8.
Cofree Modules
.................. 34
9.
Essential Extensions
................ 36
II. Categories and Functors
................ 40
1.
Categories
.................... 40
2.
Functors
..................... 44
3.
Duality
..................... 48
4.
Natural Transformations
...............50
5.
Products and Coproducts; Universal Constructions
. . 54
6.
Universal Constructions (Continued); Pull-backs
and Push-outs
.................. 59
7.
Adjoint Functors
................. 63
8.
Adjoint Functors and Universal Constructions
.... 69
9.
Abelian Categories
................ 74
10.
Projective,
Injective, and Free Objects
........ 81
HI. Extensions of Modules
................. 84
1.
Extensions
.................... 84
2.
The Functor Ext
................. 89
3.
Ext Using Injectives
................ 94
4.
Computation of some Ext-Groups
.......... 97
x
Contents
5.
Two Exact Sequences
............... 99
6.
A Theorem of Stein-Serre for Abelian Groups
..... 106
7.
The Tensor Product
................
109
8.
The Functor Tor
.................
112
IV. Derived Functors
.................... *
16
1.
Complexes
....................
117
2.
The Long Exact (Co) Homology Sequence
....... 121
3.
Homotopy
.................... 124
4.
Resolutions
....................
I26
5.
Derived Functors
................. 30
6.
The Two Long Exact Sequences of Derived Functors
. . 136
7.
The Functors Ext^ Using Projectives
......... 139
8.
The Functors
ExtJ
Using Injectives
......... 143
9.
Ext and
η
-Extensions...............
148
10.
Another Characterization of Derived Functors
.... 156
11.
The Functor Tor;?
................. 160
12.
Change of Rings
................. 162
V. The Kiinneth Formula
................. 166
1.
Double Complexes
................ 167
2.
The Kiinneth Theorem
............... 172
3.
The Dual
Künneth
Theorem
............ 177
4.
Applications of the Kiinneth Formulas
........ 180
VI. Cohomology of Groups
................. 184
1.
The Group Ring
................. 186
2.
Definition of (Co) Homology
............ 188
3.
H°,H0
......................191
4.
H Ht with Trivial Coefficient Modules
....... 192
5. The Augmentation Ideal, Derivations, and the
Semi-Direct Product
............... 194
6.
A Short Exact Sequence
.............. 197
7.
The (Co) Homology of Finite Cyclic Groups
...... 200
8.
The 5-Term Exact Sequences
............ 202
9.
Η
2,
Hopfs
Formula, and the Lower Central Series
. . . 204
10.
H2 and Extensions
................ 206
11.
Relative Projectives and Relative Injectives
...... 210
12.
Reduction Theorems
................ 213
13.
Resolutions
................... 214
14.
The (Co) Homology of a Coproduct
......... 219
Contents xi
15. The Universal
Coefficient
Theorem
and the
(CoJHomology of a Product
............ 221
16.
Groups and Subgroups
.............. 223
VII.
Cohomology of Lie Algebras
.............. 229
1.
Lie Algebras and their Universal Enveloping Algebra
. . 229
2.
Definition of Cohomology
;W°,W
.......... 234
3.
H2
and Extensions
................ 237
4.
A Resolution of the Ground Field
К
......... 239
5.
Semi-simple Lie Algebras
............. 244
6.
The two Whitehead Lemmas
............ 247
7.
Appendix: Hubert s Chain-of-Syzygies Theorem
. ... 251
VIII.
Exact Couples and Spectral Sequences
.......... 255
1.
Exact Couples and Spectral Sequences
........ 256
2.
Filtered Differential Objects
............ 261
3.
Finite Convergence Conditions for Filtered Chain
Complexes
.................... 265
4.
The Ladder of an Exact Couple
........... 269
5.
Limits
...................... 276
6.
Rees
Systems and Filtered Complexes
........ 281
7.
The Limit of a Rees System
............. 288
8.
Completions of Filtrations
............. 291
9.
The Grothendieck Spectral Sequence
......... 297
IX. Satellites and Homoiogy
................ 306
1.
Projective
Classes of Epimorphisms
......... 307
2.
^-Derived Functors
................ 309
3.
¿-Satellites
.................... 312
4.
The Adjoint Theorem and Examples
......... 318
5.
Kan Extensions and Homoiogy
........... 320
6.
Applications: Homoiogy of Small Categories,
Spectral Sequences
................ 327
X. Some Applications and Recent Developments
331
1.
Homological Algebra and Algebraic Topology
..... 331
2. Nilpotent
Groups
................. 335
3.
Finiteness Conditions on Groups
.......... 339
4.
Modular Representation Theory
........... 344
5.
Stable and Derived Categories
............ 349
xii Contents
Bibliography
......................357
Index .........................359
|
| any_adam_object | 1 |
| author | Hilton, Peter John 1923-2010 Stammbach, Urs 1939- |
| author_GND | (DE-588)115702822 (DE-588)13600279X |
| author_facet | Hilton, Peter John 1923-2010 Stammbach, Urs 1939- |
| author_role | aut aut |
| author_sort | Hilton, Peter John 1923-2010 |
| author_variant | p j h pj pjh u s us |
| building | Verbundindex |
| bvnumber | BV011222930 |
| classification_rvk | SK 320 |
| classification_tum | MAT 552f MAT 185f |
| ctrlnum | (OCoLC)845182091 (DE-599)BVBBV011222930 |
| dewey-full | 512.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.55 |
| dewey-search | 512.55 |
| dewey-sort | 3512.55 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| isbn | 0387948236 |
| language | English |
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| publishDate | 1997 |
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| series2 | Graduate texts in mathematics |
| spelling | Hilton, Peter John 1923-2010 Verfasser (DE-588)115702822 aut A course in homological algebra P. J. Hilton ; U. Stammbach 2. ed. New York [u.a.] Springer 1997 XII, 364 S. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 4 Homologische Algebra (DE-588)4160598-6 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content 2\p (DE-588)4123623-3 Lehrbuch gnd-content Homologische Algebra (DE-588)4160598-6 s DE-604 Stammbach, Urs 1939- Verfasser (DE-588)13600279X aut Graduate texts in mathematics 4 (DE-604)BV000000067 4 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007529675&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hilton, Peter John 1923-2010 Stammbach, Urs 1939- A course in homological algebra Graduate texts in mathematics Homologische Algebra (DE-588)4160598-6 gnd |
| subject_GND | (DE-588)4160598-6 (DE-588)4151278-9 (DE-588)4123623-3 |
| title | A course in homological algebra |
| title_auth | A course in homological algebra |
| title_exact_search | A course in homological algebra |
| title_full | A course in homological algebra P. J. Hilton ; U. Stammbach |
| title_fullStr | A course in homological algebra P. J. Hilton ; U. Stammbach |
| title_full_unstemmed | A course in homological algebra P. J. Hilton ; U. Stammbach |
| title_short | A course in homological algebra |
| title_sort | a course in homological algebra |
| topic | Homologische Algebra (DE-588)4160598-6 gnd |
| topic_facet | Homologische Algebra Einführung Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007529675&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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