Introduction to commutative algebra and algebraic geometry:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English German |
| Published: |
Boston [u.a.]
Birkhäuser
1985
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 238 S. graph. Darst. |
| ISBN: | 3764330651 0817630651 9780817630652 |
Staff View
MARC
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| 240 | 1 | 0 | |a Einführung in die kommutative Algebra und algebraische Geometrie |
| 245 | 1 | 0 | |a Introduction to commutative algebra and algebraic geometry |c Ernst Kunz |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 1985 | |
| 300 | |a IX, 238 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 4 | |a Algèbre commutative | |
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Record in the Search Index
| _version_ | 1804116447675285504 |
|---|---|
| adam_text | Contents
Foreword
...........................
vii
Preface
............................ ix
Preface to the English Edition
.................. ix
Terminology
..........................
χ
Chapter I. Algebraic varieties
.................. 1
§1.
Affine
algebraic varieties
................... 1
§2.
The Hubert Basis Theorem. Decomposition of a variety into
irreducible components
................. . 10
§3.
Hubert s
Nullstellensatz................... 16
§4.
The spectrum of a ring
.................. . 22
§5.
Projective
varieties and the homogeneous spectrum
....... 29
References
........................... 38
Chapter II. Dimension
..................... 39
§1.
The Krull dimension of topological spaces and rings
....... 39
§2.
Prime ideal chains and integral ring extensions
......... 44
§3.
The dimension of
affine
algebras and
affine
algebraic varieties
. . 49
§4.
The dimension of
projective
varieties
............. 59
References
........................... 61
Chapter III. Regular and rational functions on algebraic varieties.
Localization
....................... 63
§1.
Some properties of the Zariski topology
............ 63
§2.
The sheaf of regular functions on an algebraic variety
...... 66
§3.
Rings and modules of fractions. Examples
........... 73
§4.
Properties of rings and modules of fractions
.......... 78
§5.
The fiber sum and fiber product of modules. Gluing modules
. . 88
References
........................... 92
Chapter IV. The local-global principle in commutative algebra
.... 93
§1.
The passage from local to global
.............. . 93
§2.
The generation of modules and ideals
............. 104
§3.
Projective
modules
..................... 110
References
........................... 122
vi
TABLE OF CONTENTS
Chapter V. On the number of equations needed to describe an
algebraic variety
..................... 123
§1.
Any variety in w-dimensional space is the intersection of
η
hypersurfaces
...................... 123
§2.
Rings and modules of finite length
.............. 127
§3.
Krulľs
Principal Ideal Theorem. Dimension of the intersection
of two varieties
...................... 130
§4.
Applications of the Principal Ideal Theorem in Noetherian rings
. 141
§5.
The graded ring and the conormal module of an ideal
...... 149
References
........................... 162
Chapter VI. Regular and singular points of algebraic varieties
.... 163
§1.
Regular points of algebraic varieties. Regular local rings
..... 163
§2.
The zero divisiors of a ring or module. Primary decomposition
. . 176
§3.
Regular sequences. Cohen-Macaulay modules and rings
..... 183
§4.
A connectedness theorem for set-theoretic complete intersections
in
projective
space
.................... 192
References
........................... 194
Chapter
VII.
Projective
Resolutions
............... 196
§1.
The
projective
dimension of modules
............. 196
§2.
Homological characterizations of regular rings and local
complete intersections
................... 205
§3.
Modules of
projective
dimension
< 1 ............. 211
§4.
Algebraic curves in A3 that are locally complete intersections
can be represented as the intersection of two algebraic surfaces
. 219
References
........................... 222
Bibliography
.......................... 224
A. Textbooks
......................... 224
B. Research papers
...................... 225
List of symbols
......................... 229
Index
............................. 232
|
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| dewey-ones | 512 - Algebra |
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| dewey-sort | 3512 224 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV002000085 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:38:39Z |
| institution | BVB |
| isbn | 3764330651 0817630651 9780817630652 |
| language | English German |
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| physical | IX, 238 S. graph. Darst. |
| publishDate | 1985 |
| publishDateSearch | 1985 |
| publishDateSort | 1985 |
| publisher | Birkhäuser |
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| spelling | Kunz, Ernst 1933-2021 Verfasser (DE-588)138730083 aut Einführung in die kommutative Algebra und algebraische Geometrie Introduction to commutative algebra and algebraic geometry Ernst Kunz Boston [u.a.] Birkhäuser 1985 IX, 238 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Algèbre commutative Géométrie algébrique Commutative algebra Geometry, Algebraic Kommutative Algebra (DE-588)4164821-3 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Algebraische Geometrie (DE-588)4001161-6 s Kommutative Algebra (DE-588)4164821-3 s 2\p DE-604 DE-604 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001304663&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 | Kunz, Ernst 1933-2021 Introduction to commutative algebra and algebraic geometry Algèbre commutative Géométrie algébrique Commutative algebra Geometry, Algebraic Kommutative Algebra (DE-588)4164821-3 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| subject_GND | (DE-588)4164821-3 (DE-588)4001161-6 (DE-588)4151278-9 |
| title | Introduction to commutative algebra and algebraic geometry |
| title_alt | Einführung in die kommutative Algebra und algebraische Geometrie |
| title_auth | Introduction to commutative algebra and algebraic geometry |
| title_exact_search | Introduction to commutative algebra and algebraic geometry |
| title_full | Introduction to commutative algebra and algebraic geometry Ernst Kunz |
| title_fullStr | Introduction to commutative algebra and algebraic geometry Ernst Kunz |
| title_full_unstemmed | Introduction to commutative algebra and algebraic geometry Ernst Kunz |
| title_short | Introduction to commutative algebra and algebraic geometry |
| title_sort | introduction to commutative algebra and algebraic geometry |
| topic | Algèbre commutative Géométrie algébrique Commutative algebra Geometry, Algebraic Kommutative Algebra (DE-588)4164821-3 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| topic_facet | Algèbre commutative Géométrie algébrique Commutative algebra Geometry, Algebraic Kommutative Algebra Algebraische Geometrie Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001304663&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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