Commutative algebra:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Reading, Mass. [u.a.]
Benjamin
1980
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Mathematics lecture note series
56 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 313 S. |
| ISBN: | 0805370269 |
Internformat
MARC
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| 100 | 1 | |a Matsumura, Hideyuki |d 1930- |e Verfasser |0 (DE-588)13778161X |4 aut | |
| 245 | 1 | 0 | |a Commutative algebra |c Hideyuki Matsumura |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Reading, Mass. [u.a.] |b Benjamin |c 1980 | |
| 300 | |a XV, 313 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics lecture note series |v 56 | |
| 650 | 4 | |a Algèbre commutative | |
| 650 | 7 | |a Algèbre commutative |2 ram | |
| 650 | 4 | |a Commutative algebra | |
| 650 | 0 | 7 | |a Algebraische Geometrie |0 (DE-588)4001161-6 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804116723471745024 |
|---|---|
| adam_text | Contents
Preface to the First Edition xi
Preface to the Second Edition xiii
Conventions xv
PARTI
Chapter 1. ELEMENTARY RESULTS
1. General Rings 1
2. Noetherian Rings and Artinian Rings 13
Chapter 2. FLATNESS
3. Flatness 17
4. Faithful Flatness 25
5. Going-up Theorem and Going-down Theorem 31
6. Constructibe Sets 38
Chapter 3. ASSOCIATED PRIMES
7. Ass(M) 49
8. Primary Decomposition 52
9. Homomorphisms and Ass 57
Chapter 4. GRADED RINGS
10. Graded Rings and Modules 61
11. Artin-Rees Theorem 67
Chapter 5. DIMENSION
12. Dimension 71
13. Homomorphisms and Dimension 78
14. Finitely Generated Extensions 83
Chapter 6. DEPTH
15. M-regular Sequences 95
16. Cohen-Macaulay Rings 106
Chapter 7. NORMAL RINGS AND REGULAR RINGS
17. Classical Theory 115
18. Homological Theory 127
19. Unique Factorization 141
ix
x Contents
Chapter 8. FLATNESS II
20. Local Criteria of Flatness 145
21. Fibres of Flat Morphisms 152
22. Theorem of Generic Flatness 156
Chapter 9. COMPLETION
23. Completion 161
24. Zariski Rings 172
PART II
Chapter 10. DERIVATION
25. Extension of a Ring by a Module 177
26. Derivations and Differentials 180
27. Separability 190
Chapter 11. FORMAL SMOOTHNESS
28. Formal Smoothness I 197
29. Jacobian Criteria 213
30. Formal Smoothness II 222
Chapter 12. NAGATA RINGS
31. Nagata Rings 231
Chapter 13. EXCELLENT RINGS
32. Closedness of Singular Locus 245
33. Formal Libres and G-Rings 249
34. Excellent Rings 258
APPENDIX
3 5. Eakin s Theorem 261
36. A Flatness Theorem 263
37. Coefficient Rings 265
38. p-Basis 269
39. Cartier s Equality and Geometric Regularity 278
40. Jacobian Criteria and Excellent Rings 281
41. Krull Rings and Marot s Theorem 293
42. Kunz Theorems 299
43. Complement 306
Index 311
Index of Symbols 313
|
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| author | Matsumura, Hideyuki 1930- |
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| bvnumber | BV002265768 |
| callnumber-first | Q - Science |
| callnumber-label | QA251 |
| callnumber-raw | QA251.3 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 230 |
| ctrlnum | (OCoLC)6086627 (DE-599)BVBBV002265768 |
| dewey-full | 512/.24 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.24 |
| dewey-search | 512/.24 |
| dewey-sort | 3512 224 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV002265768 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:43:02Z |
| institution | BVB |
| isbn | 0805370269 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001488911 |
| oclc_num | 6086627 |
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| physical | XV, 313 S. |
| psigel | TUB-nvmb |
| publishDate | 1980 |
| publishDateSearch | 1980 |
| publishDateSort | 1980 |
| publisher | Benjamin |
| record_format | marc |
| series | Mathematics lecture note series |
| series2 | Mathematics lecture note series |
| spelling | Matsumura, Hideyuki 1930- Verfasser (DE-588)13778161X aut Commutative algebra Hideyuki Matsumura 2. ed. Reading, Mass. [u.a.] Benjamin 1980 XV, 313 S. txt rdacontent n rdamedia nc rdacarrier Mathematics lecture note series 56 Algèbre commutative Algèbre commutative ram Commutative algebra Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Kommutative Algebra (DE-588)4164821-3 gnd rswk-swf Kommutative Algebra (DE-588)4164821-3 s DE-604 Algebraische Geometrie (DE-588)4001161-6 s 1\p DE-604 Mathematics lecture note series 56 (DE-604)BV001899001 56 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001488911&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 algebra Mathematics lecture note series Algèbre commutative Algèbre commutative ram Commutative algebra Algebraische Geometrie (DE-588)4001161-6 gnd Kommutative Algebra (DE-588)4164821-3 gnd |
| subject_GND | (DE-588)4001161-6 (DE-588)4164821-3 |
| title | Commutative algebra |
| title_auth | Commutative algebra |
| title_exact_search | Commutative algebra |
| title_full | Commutative algebra Hideyuki Matsumura |
| title_fullStr | Commutative algebra Hideyuki Matsumura |
| title_full_unstemmed | Commutative algebra Hideyuki Matsumura |
| title_short | Commutative algebra |
| title_sort | commutative algebra |
| topic | Algèbre commutative Algèbre commutative ram Commutative algebra Algebraische Geometrie (DE-588)4001161-6 gnd Kommutative Algebra (DE-588)4164821-3 gnd |
| topic_facet | Algèbre commutative Commutative algebra Algebraische Geometrie Kommutative Algebra |
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