Commutative ring theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2005
|
| Ausgabe: | 1. paperback ed. (with corr.), reprinted |
| Schriftenreihe: | Cambridge studies in advanced mathematics
8 |
| Schlagworte: | |
| Online-Zugang: | http://www.gbv.de/dms/bowker/toc/9780521367646.pdf Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke. - Aus dem Japan. übers. |
| Beschreibung: | XIII, 320 S. |
| ISBN: | 9780521367646 0521367646 |
Internformat
MARC
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| 245 | 1 | 0 | |a Commutative ring theory |c Hideyuki Matsumura |
| 250 | |a 1. paperback ed. (with corr.), reprinted | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2005 | |
| 300 | |a XIII, 320 S. | ||
| 336 | |b txt |2 rdacontent | ||
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Datensatz im Suchindex
| _version_ | 1804134677138636800 |
|---|---|
| adam_text | Contents
Preface
vii
Introduction
ix
Conventions and terminology
xiii
1
Commutative rings and modules
1
1
Ideals
1
2
Modules
6
3
Chain conditions
14
2
Prime ideals
20
4
Localisation and Spec of a ring
20
5
The
Hubert
Nullstellensatz and first steps in dimension theory
30
6
Associated primes and primary decomposition
37
Appendix to
§6.
Secondary representations of a module
42
3
Properties of extension rings
45
7
Flatness
45
Appendix to
§7.
Pure
submodules
S3
8
Completion and the Artin-Rees lemma
55
9
Integral extensions
64
4
Valuation rings
71
10
General valuations
71
11
DVRs and Dedekind rings
78
12
Krull rings
86
5
Dimension theory
92
13
Graded rings, the Hubert function and the Samuel function
92
Appendix to
§13.
Determinantul
ideals
103
14
Systems of parameters and multiplicity
104
15
The dimension of extension rings
116
6
Regular sequences
123
16
Regular sequences and the
Koszul
complex
123
17
Cohen-Macaulay rings
133
18
Gorenstein rings
139
7
Regular rings
153
19
Regular rings
153
20
UFDs
161
21
Complete intersection rings
169
vi
Contents
8
Flatness revisited
173
22
The local flatness criterion
173
23
Flatness and Fibres
178
24
Generic freeness and open loci results
185
9
Derivations
190
25
Derivations and differentials
190
26
Separability
198
27
Higher derivations
207
10
I-smoothness
213
28
/-smoothness
213
29
The structure theorems for complete local rings
223
30
Connections with derivations
230
11
Applications of complete local rings
246
31
Chains of prime ideals
246
32
The formal fibre
255
33
Some other applications
261
Appendix A. Tensor products, direct and inverse limits
266
Appendix B. Some homological algebra T7A
Appendix C. The exterior algebra
283
Solutions and hints for exercises
287
References
298
Index
315
|
| adam_txt |
Contents
Preface
vii
Introduction
ix
Conventions and terminology
xiii
1
Commutative rings and modules
1
1
Ideals
1
2
Modules
6
3
Chain conditions
14
2
Prime ideals
20
4
Localisation and Spec of a ring
20
5
The
Hubert
Nullstellensatz and first steps in dimension theory
30
6
Associated primes and primary decomposition
37
Appendix to
§6.
Secondary representations of a module
42
3
Properties of extension rings
45
7
Flatness
45
Appendix to
§7.
Pure
submodules
S3
8
Completion and the Artin-Rees lemma
55
9
Integral extensions
64
4
Valuation rings
71
10
General valuations
71
11
DVRs and Dedekind rings
78
12
Krull rings
86
5
Dimension theory
92
13
Graded rings, the Hubert function and the Samuel function
92
Appendix to
§13.
Determinantul
ideals
103
14
Systems of parameters and multiplicity
104
15
The dimension of extension rings
116
6
Regular sequences
123
16
Regular sequences and the
Koszul
complex
123
17
Cohen-Macaulay rings
133
18
Gorenstein rings
139
7
Regular rings
153
19
Regular rings
153
20
UFDs
161
21
Complete intersection rings
169
vi
Contents
8
Flatness revisited
173
22
The local flatness criterion
173
23
Flatness and Fibres
178
24
Generic freeness and open loci results
185
9
Derivations
190
25
Derivations and differentials
190
26
Separability
198
27
Higher derivations
207
10
I-smoothness
213
28
/-smoothness
213
29
The structure theorems for complete local rings
223
30
Connections with derivations
230
11
Applications of complete local rings
246
31
Chains of prime ideals
246
32
The formal fibre
255
33
Some other applications
261
Appendix A. Tensor products, direct and inverse limits
266
Appendix B. Some homological algebra T7A
Appendix C. The exterior algebra
283
Solutions and hints for exercises
287
References
298
Index
315 |
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| author | Matsumura, Hideyuki 1930- |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 1. paperback ed. (with corr.), reprinted |
| format | Book |
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| id | DE-604.BV021233648 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T13:29:08Z |
| indexdate | 2024-07-09T20:28:24Z |
| institution | BVB |
| isbn | 9780521367646 0521367646 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014276439 |
| oclc_num | 255581597 |
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| owner | DE-355 DE-BY-UBR |
| owner_facet | DE-355 DE-BY-UBR |
| physical | XIII, 320 S. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge studies in advanced mathematics |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Matsumura, Hideyuki 1930- Verfasser (DE-588)13778161X aut Kakan kan ron Commutative ring theory Hideyuki Matsumura 1. paperback ed. (with corr.), reprinted Cambridge [u.a.] Cambridge Univ. Press 2005 XIII, 320 S. txt rdacontent n rdamedia nc rdacarrier Cambridge studies in advanced mathematics 8 Hier auch später erschienene, unveränderte Nachdrucke. - Aus dem Japan. übers. Ringtheorie (DE-588)4126571-3 gnd rswk-swf Kommutativer Ring (DE-588)4164825-0 gnd rswk-swf Ringtheorie (DE-588)4126571-3 s DE-604 Kommutativer Ring (DE-588)4164825-0 s 1\p DE-604 Cambridge studies in advanced mathematics 8 (DE-604)BV000003678 8 http://www.gbv.de/dms/bowker/toc/9780521367646.pdf Inhalt Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014276439&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 |
| spellingShingle | Matsumura, Hideyuki 1930- Commutative ring theory Cambridge studies in advanced mathematics Ringtheorie (DE-588)4126571-3 gnd Kommutativer Ring (DE-588)4164825-0 gnd |
| subject_GND | (DE-588)4126571-3 (DE-588)4164825-0 |
| title | Commutative ring theory |
| title_alt | Kakan kan ron |
| title_auth | Commutative ring theory |
| title_exact_search | Commutative ring theory |
| title_exact_search_txtP | Commutative ring theory |
| title_full | Commutative ring theory Hideyuki Matsumura |
| title_fullStr | Commutative ring theory Hideyuki Matsumura |
| title_full_unstemmed | Commutative ring theory Hideyuki Matsumura |
| title_short | Commutative ring theory |
| title_sort | commutative ring theory |
| topic | Ringtheorie (DE-588)4126571-3 gnd Kommutativer Ring (DE-588)4164825-0 gnd |
| topic_facet | Ringtheorie Kommutativer Ring |
| url | http://www.gbv.de/dms/bowker/toc/9780521367646.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014276439&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003678 |
| work_keys_str_mv | AT matsumurahideyuki kakankanron AT matsumurahideyuki commutativeringtheory |