Local algebra:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English French |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2000
|
| Schriftenreihe: | Springer monographs in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 123 - 126 |
| Beschreibung: | XIII, 128 S. |
| ISBN: | 3540666419 9783540666417 |
Internformat
MARC
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| 100 | 1 | |a Serre, Jean-Pierre |d 1926- |e Verfasser |0 (DE-588)142283126 |4 aut | |
| 240 | 1 | 0 | |a Algèbre locale |
| 245 | 1 | 0 | |a Local algebra |c Jean-Pierre Serre. Transl. from the French by CheeWhye Chin |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2000 | |
| 300 | |a XIII, 128 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer monographs in mathematics | |
| 500 | |a Literaturverz. S. 123 - 126 | ||
| 650 | 4 | |a Stellenalgebra - Kommutative Algebra | |
| 650 | 4 | |a Dimension theory (Algebra) | |
| 650 | 4 | |a Geometry, Algebraic | |
| 650 | 4 | |a Local rings | |
| 650 | 4 | |a Modules (Algebra) | |
| 650 | 0 | 7 | |a Kommutative Algebra |0 (DE-588)4164821-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Stellenalgebra |0 (DE-588)4183082-9 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804127878511591424 |
|---|---|
| adam_text | Contents
Preface v
Contents vii
Introduction xi
I. Prime Ideals and Localization 1
§ 1. Notation and definitions 1
§2. Nakayama s lemma 1
§3. Localization 2
§4. Noetherian rings and modules 4
§5. Spectrum 4
§6. The noetherian case 5
§7. Associated prime ideals 6
§8. Primary decompositions 10
II. Tools 11
A: Filtrations and Gradings 11
§1. Filtered rings and modules 11
§2. Topology defined by a filtration 12
§3. Completion of filtered modules 13
§4. Graded rings and modules 14
§5. Where everything becomes noetherian again —
q adic filtrations 17
B: Hilbert Samuel Polynomials 19
§1. Review on integer valued polynomials 19
§2. Polynomial like functions 21
§3. The Hilbert polynomial 21
§4. The Samuel polynomial 24
viii Contents
III. Dimension Theory 29
A: Dimension of Integral Extensions 29
§1. Definitions 29
§2. Cohen Seidenberg first theorem 30
§3. Cohen Seidenberg second theorem 32
B: Dimension in Noetherian Rings 33
§1. Dimension of a module 33
§2. The case of noetherian local rings 33
§3. Systems of parameters 36
C: Normal Rings 37
§1. Characterization of normal rings 37
§2. Properties of normal rings 38
§3. Integral closure 40
D: Polynomial Rings 40
§1. Dimension of the ring A[Xi,... , Xn] 40
§2. The normalization lemma 42
§3. Applications. I. Dimension in polynomial algebras .... 44
§4. Applications. II. Integral closure of a finitely
generated algebra 46
§5. Applications. III. Dimension of an intersection in
affine space 47
IV. Homological Dimension and Depth 51
A: The Koszul Complex 51
§1. The simple case 51
§2. Acyclicity and functorial properties of the Koszul
complex 53
§3. Filtration of a Koszul complex 56
§4. The depth of a module over a noetherian local ring ... 59
B: Cohen Macaulay Modules 62
§1. Definition of Cohen Macaulay modules 63
§2. Several characterizations of Cohen Macaulay
modules 64
§3. The support of a Cohen Macaulay module 66
§4. Prime ideals and completion 68
C: Homological Dimension and Noetherian Modules 70
§1. The homological dimension of a module 70
§2. The noetherian case 71
§3. The local case 73
Contents ix
D: Regular Rings 75
§1. Properties and characterizations of regular local
rings 75
§2. Permanence properties of regular local rings 78
§3. Delocalization 80
§4. A criterion for normality 82
§5. Regularity in ring extensions 83
Appendix I: Minimal Resolutions 84
§1. Definition of minimal resolutions 84
§2. Application 85
§3. The case of the Koszul complex 86
Appendix II: Positivity of Higher Euler Poincare
Characteristics 88
Appendix III: Graded polynomial Algebras 91
§1. Notation 91
§2. Graded polynomial algebras 92
§3. A characterization of graded polynomial algebras 93
§4. Ring extensions 93
§5. Application: the Shephard Todd theorem 95
V. Multiplicities 99
A: Multiplicity of a Module 99
§1. The group of cycles of a ring 99
§2. Multiplicity of a module 100
B: Intersection Multiplicity of Two Modules 101
§1. Reduction to the diagonal 101
§2. Completed tensor products 102
§3. Regular rings of equal characteristic 106
§4. Conjectures 107
§5. Regular rings of unequal characteristic (unramified
case) 108
§6. Arbitrary regular rings 110
C: Connection with Algebraic Geometry 112
§1. Tor formula 112
§2. Cycles on a non singular affine variety 113
§3. Basic formulae 114
§4. Proof of theorem 1 116
§5. Rationality of intersections 116
x Contents
§6. Direct images 117
§7. Pull backs 117
§8. Extensions of intersection theory 119
Bibliography 123
Index 127
Index of Notation 129
|
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 230 |
| ctrlnum | (OCoLC)247279027 (DE-599)BVBBV013177632 |
| dewey-full | 516.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.35 |
| dewey-search | 516.35 |
| dewey-sort | 3516.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV013177632 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:40:21Z |
| institution | BVB |
| isbn | 3540666419 9783540666417 |
| language | English French |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008978737 |
| oclc_num | 247279027 |
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| owner_facet | DE-355 DE-BY-UBR DE-703 DE-19 DE-BY-UBM DE-384 DE-M347 DE-706 DE-634 DE-83 DE-11 DE-188 DE-29T |
| physical | XIII, 128 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer monographs in mathematics |
| spelling | Serre, Jean-Pierre 1926- Verfasser (DE-588)142283126 aut Algèbre locale Local algebra Jean-Pierre Serre. Transl. from the French by CheeWhye Chin Berlin [u.a.] Springer 2000 XIII, 128 S. txt rdacontent n rdamedia nc rdacarrier Springer monographs in mathematics Literaturverz. S. 123 - 126 Stellenalgebra - Kommutative Algebra Dimension theory (Algebra) Geometry, Algebraic Local rings Modules (Algebra) Kommutative Algebra (DE-588)4164821-3 gnd rswk-swf Stellenalgebra (DE-588)4183082-9 gnd rswk-swf Stellenalgebra (DE-588)4183082-9 s Kommutative Algebra (DE-588)4164821-3 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008978737&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Serre, Jean-Pierre 1926- Local algebra Stellenalgebra - Kommutative Algebra Dimension theory (Algebra) Geometry, Algebraic Local rings Modules (Algebra) Kommutative Algebra (DE-588)4164821-3 gnd Stellenalgebra (DE-588)4183082-9 gnd |
| subject_GND | (DE-588)4164821-3 (DE-588)4183082-9 |
| title | Local algebra |
| title_alt | Algèbre locale |
| title_auth | Local algebra |
| title_exact_search | Local algebra |
| title_full | Local algebra Jean-Pierre Serre. Transl. from the French by CheeWhye Chin |
| title_fullStr | Local algebra Jean-Pierre Serre. Transl. from the French by CheeWhye Chin |
| title_full_unstemmed | Local algebra Jean-Pierre Serre. Transl. from the French by CheeWhye Chin |
| title_short | Local algebra |
| title_sort | local algebra |
| topic | Stellenalgebra - Kommutative Algebra Dimension theory (Algebra) Geometry, Algebraic Local rings Modules (Algebra) Kommutative Algebra (DE-588)4164821-3 gnd Stellenalgebra (DE-588)4183082-9 gnd |
| topic_facet | Stellenalgebra - Kommutative Algebra Dimension theory (Algebra) Geometry, Algebraic Local rings Modules (Algebra) Kommutative Algebra Stellenalgebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008978737&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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