Relative homological algebra:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; New York
<<de>> Gruyter
2000
|
| Series: | De Gruyter expositions in mathematics
30 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 321 - 330 |
| Physical Description: | XI, 339 S. |
| ISBN: | 311016633X |
Staff View
MARC
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| 100 | 1 | |a Enochs, Edgar E. |d 1932- |e Verfasser |0 (DE-588)121759253 |4 aut | |
| 245 | 1 | 0 | |a Relative homological algebra |c by Edgar E. Enochs ; Overtoun M. G. Jenda |
| 264 | 1 | |a Berlin ; New York |b <<de>> Gruyter |c 2000 | |
| 300 | |a XI, 339 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter expositions in mathematics |v 30 | |
| 500 | |a Literaturverz. S. 321 - 330 | ||
| 650 | 7 | |a Algèbre homologique |2 ram | |
| 650 | 4 | |a Algebra, Homological | |
| 650 | 0 | 7 | |a Homologische Algebra |0 (DE-588)4160598-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Homologische Algebra |0 (DE-588)4160598-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Jenda, Overtoun M. G. |e Verfasser |0 (DE-588)12175927X |4 aut | |
| 830 | 0 | |a De Gruyter expositions in mathematics |v 30 |w (DE-604)BV004069300 |9 30 | |
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Record in the Search Index
| _version_ | 1807772849496129536 |
|---|---|
| adam_text |
CONTENTS
PREFACE
VII
1
BASIC
CONCEPTS
1
1.1
ZORN
'
S
LEMMA,
ORDINAL
AND
CARDINAL
NUMBERS
.
1
1.2
MODULES
.
7
1.3
CATEGORIES
AND
FUNCTORS
.
17
1.4
COMPLEXES
OF
MODULES
AND
HOMOLOGY
.
25
1.5
DIRECT
AND
INVERSE
LIMITS
.
31
1.6
/-ADIC
TOPOLOGY
AND
COMPLETIONS
.
36
2
FLAT
MODULES,
CHAIN
CONDITIONS
AND
PRIME
IDEALS
40
2.1
FLAT
MODULES
.
40
2.2
LOCALIZATION
.
44
2.3
CHAIN
CONDITIONS
.
46
2.4
PRIME
IDEALS
AND
PRIMARY
DECOMPOSITION
.
51
2.5
ARTIN-REES
LEMMA
AND
ZARISKI
RINGS
.
61
3
INJECTIVE
AND
FLAT
MODULES
68
3.1
INJECTIVE
MODULES
.
68
3.2
NATURAL
IDENTITIES,
FLAT
MODULES,
AND
INJECTIVE
MODULES
.
75
3.3
INJECTIVE
MODULES
OVER
COMMUTATIVE
NOETHERIAN
RINGS
.
84
3.4
MATLIS
DUALITY
.
88
4
TORSION
FREE
COVERING
MODULES
93
4.1
EXISTENCE
OF
TORSION
FREE
PRECOVERS
.
93
4.2
EXISTENCE
OF
TORSION
FREE
COVERS
.
95
4.3
EXAMPLES
.
97
4.4
DIRECT
SUMS
AND
PRODUCTS
.
101
5
COVERS
105
5.1
^-PRECOVERS
AND
COVERS
.
105
5.2
EXISTENCE
OF
PRECOVERS
AND
COVERS
.
107
5.3
PROJECTIVE
AND
FLAT
COVERS
.
110
5.4
INJECTIVE
COVERS
.
120
5.5
DIRECT
SUMS
AND
T-NILPOTENCY
.
125
X
CONTENTS
6
ENVELOPES
129
6.1
.F-PREENVELOPES
AND
ENVELOPES
.
129
6.2
EXISTENCE
OF
PREENVELOPES
.
130
6.3
EXISTENCE
OF
ENVELOPES
.
132
6.4
DIRECT
SUMS
OF
ENVELOPES
.
134
6.5
FLAT
ENVELOPES
.
136
6.6
EXISTENCE
OF
ENVELOPES
FOR
INJECTIVE
STRUCTURES
.
139
6.7
PURE
INJECTIVE
ENVELOPES
.
144
7
COVERS,
ENVELOPES,
AND
COTORSION
THEORIES
152
7.1
DEFINITIONS
AND
BASIC
RESULTS
.
152
7.2
FIBRATIONS,
COFIBRATIONS
AND
WAKAMATSU
LEMMAS
.
154
7.3
SET
THEORETIC
HOMOLOGICAL
ALGEBRA
.
160
7.4
COTORSION
THEORIES
WITH
ENOUGH
INJECTIVES
AND
PROJECTIVES
.
162
8
RELATIVE
HOMOLOGICAL
ALGEBRA
AND
BALANCE
167
8.1
LEFT
AND
RIGHT
^-RESOLUTIONS
.
167
8.2
DERIVED
FUNCTORS
AND
BALANCE
.
169
8.3
APPLICATIONS
TO
MODULES
.
177
8.4
/'-DIMENSIONS
.
180
8.5
MINIMAL
PURE
INJECTIVE
RESOLUTIONS
OF
FLAT
MODULES
.
194
8.6
X
AND
FJ,
-DIMENSIONS
.
203
9
IWANAGA-GORENSTEIN
AND
COHEN-MACAULAY
RINGS
AND
THEIR
MODULES
211
9.1
IWANAGA-GORENSTEIN
RINGS
.
211
9.2
THE
MINIMAL
INJECTIVE
RESOLUTION
OF
R
.
215
9.3
MORE
ON
FLAT
AND
INJECTIVE
MODULES
.
223
9.4
TORSION
PRODUCTS
OF
INJECTIVE
MODULES
.
226
9.5
LOCAL
COHOMOLOGY
AND
THE
DUALIZING
MODULE
.
229
10
GORENSTEIN
MODULES
239
10.1
GORENSTEIN
INJECTIVE
MODULES
.
239
10.2
GORENSTEIN
PROJECTIVE
MODULES
.
246
10.3
GORENSTEIN
FLAT
MODULES
.
253
10.4
FOXBY
CLASSES
.
258
11
GORENSTEIN
COVERS
AND
ENVELOPES
269
11.1
GORENSTEIN
INJECTIVE
PRECOVERS
AND
COVERS
.
269
11.2
GORENSTEIN
INJECTIVE
PREENVELOPES
.
270
11.3
GORENSTEIN
INJECTIVE
ENVELOPES
.
274
11.4
GORENSTEIN
ESSENTIAL
EXTENSIONS
.
277
11.5
GORENSTEIN
PROJECTIVE
PRECOVERS
AND
COVERS
.
279
11.6
AUSLANDER
'
S
LAST
THEOREM
(GORENSTEIN
PROJECTIVE
COVERS)
.
284
11.7
GORENSTEIN
FLAT
COVERS
.
288
CONTENTS
XI
11.8
GORENSTEIN
FLAT
AND
PROJECTIVE
PREENVELOPES
.
292
12
BALANCE
OVER
GORENSTEIN
AND
COHEN-MACAULAY
RINGS
294
12.1
BALANCE
OF
HOM(
-
,
-
)
.
294
12.2
BALANCE
OF
-
-
.
298
12.3
DIMENSIONS
OVER
N
-GORENSTEIN
RINGS
.
300
12.4
DIMENSIONS
OVER
COHEN-MACAULAY
RINGS
.
305
12.5
Q-GORENSTEIN
MODULES
.
307
BIBLIOGRAPHICAL
NOTES
319
BIBLIOGRAPHY
321
INDEX
331 |
| any_adam_object | 1 |
| author | Enochs, Edgar E. 1932- Jenda, Overtoun M. G. |
| author_GND | (DE-588)121759253 (DE-588)12175927X |
| author_facet | Enochs, Edgar E. 1932- Jenda, Overtoun M. G. |
| author_role | aut aut |
| author_sort | Enochs, Edgar E. 1932- |
| author_variant | e e e ee eee o m g j omg omgj |
| building | Verbundindex |
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| callnumber-search | QA169 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 260 SK 320 |
| ctrlnum | (OCoLC)43167922 (DE-599)BVBBV013038249 |
| 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 255 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV013038249 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-19T00:15:34Z |
| institution | BVB |
| isbn | 311016633X |
| language | English |
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| owner_facet | DE-739 DE-824 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-11 |
| physical | XI, 339 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | <<de>> Gruyter |
| record_format | marc |
| series | De Gruyter expositions in mathematics |
| series2 | De Gruyter expositions in mathematics |
| spelling | Enochs, Edgar E. 1932- Verfasser (DE-588)121759253 aut Relative homological algebra by Edgar E. Enochs ; Overtoun M. G. Jenda Berlin ; New York <<de>> Gruyter 2000 XI, 339 S. txt rdacontent n rdamedia nc rdacarrier De Gruyter expositions in mathematics 30 Literaturverz. S. 321 - 330 Algèbre homologique ram Algebra, Homological Homologische Algebra (DE-588)4160598-6 gnd rswk-swf Homologische Algebra (DE-588)4160598-6 s DE-604 Jenda, Overtoun M. G. Verfasser (DE-588)12175927X aut De Gruyter expositions in mathematics 30 (DE-604)BV004069300 30 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008882886&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Enochs, Edgar E. 1932- Jenda, Overtoun M. G. Relative homological algebra De Gruyter expositions in mathematics Algèbre homologique ram Algebra, Homological Homologische Algebra (DE-588)4160598-6 gnd |
| subject_GND | (DE-588)4160598-6 |
| title | Relative homological algebra |
| title_auth | Relative homological algebra |
| title_exact_search | Relative homological algebra |
| title_full | Relative homological algebra by Edgar E. Enochs ; Overtoun M. G. Jenda |
| title_fullStr | Relative homological algebra by Edgar E. Enochs ; Overtoun M. G. Jenda |
| title_full_unstemmed | Relative homological algebra by Edgar E. Enochs ; Overtoun M. G. Jenda |
| title_short | Relative homological algebra |
| title_sort | relative homological algebra |
| topic | Algèbre homologique ram Algebra, Homological Homologische Algebra (DE-588)4160598-6 gnd |
| topic_facet | Algèbre homologique Algebra, Homological Homologische Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008882886&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004069300 |
| work_keys_str_mv | AT enochsedgare relativehomologicalalgebra AT jendaovertounmg relativehomologicalalgebra |