Introduction to commutative algebra:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | Undetermined |
| Veröffentlicht: |
Reading, Mass. [u.a.]
Addison-Wesley
[2010]
|
| Ausgabe: | [reprint.] |
| Schriftenreihe: | Addison-Wesley series in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 128 S. |
| ISBN: | 0201407515 9780201407518 |
Internformat
MARC
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| 100 | 1 | |a Atiyah, Michael Francis |d 1929-2019 |e Verfasser |0 (DE-588)118848453 |4 aut | |
| 245 | 1 | 0 | |a Introduction to commutative algebra |c M. F. Atiyah ; I. G. MacDonald |
| 250 | |a [reprint.] | ||
| 264 | 1 | |a Reading, Mass. [u.a.] |b Addison-Wesley |c [2010] | |
| 300 | |a 128 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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| 650 | 0 | 7 | |a Ring |g Mathematik |0 (DE-588)4128084-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kommutative Algebra |0 (DE-588)4164821-3 |2 gnd |9 rswk-swf |
| 655 | 7 | |8 1\p |0 (DE-588)4151278-9 |a Einführung |2 gnd-content | |
| 689 | 0 | 0 | |a Kommutative Algebra |0 (DE-588)4164821-3 |D s |
| 689 | 0 | 1 | |a Ring |g Mathematik |0 (DE-588)4128084-2 |D s |
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| 700 | 1 | |a Macdonald, Ian G. |d 1928- |e Verfasser |0 (DE-588)123369258 |4 aut | |
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Datensatz im Suchindex
| _version_ | 1804141164027183104 |
|---|---|
| adam_text | Contents
Introduction
......
,
.........
vìi
Notation and Terminology
............ ix
Chapter
1
Rings and Ideals
............... 1
Rings and ring bomomorphisms
.......... 1
Ideals. Quotient rings
............. 2
Zero-divisors.
Nilpotent
elements. Units
........ 2
Prime ideals and maximal ideals
.......... 3
Nilradical and
Jacobson
radical
. ....... 5
Operations on ideals
............. 6
Extension and contraction
............ 9
Exercises
................ 10
Chapter
2
Modales
................. 17
Modules and module homomorphisms
........ 17
Submodules
and quotient modules
......... 18
Operations on
submodules
............ 19
Direct sum and product
............ 20
Finitely generated modules
.......... 21
Exact sequences
............... 22
Tensor product of modules
..........· 24
Restriction and extension of scalars
......... 27
Exactness properties of the tensor product
....... 28
Algebras
.... .............. 29
Tensor product of algebras
........... 30
Exercises
................. 31
Chapter
3
Rings and Modules of Fractions
.......... 36
Local properties
............... 40
Extended and contracted ideals in rings of fractions
.... 41
Exercises
................. 43
Chapter
4
Primary Decomposition
............
SO
Exercises
................. 55
ν
Chapter
5
Integral Dependence and Valuations
......... 59
Integra] dependence
............. 59
The going-up theorem
............. 61
Integrally closed integral domains. The going-down theorem.
. 62
Valuation rings
............... 65
Exercises
................. 67
Chapter
6
Chain Conditions
.............. 74
Exercises
................. 78
Chapter
7
Noetherian Rings
.............. 80
Primary decomposition in Noetherian rings
...... 82
Exercises
................. 84
Chapter
8 Artin
Rings
................ 89
Exercises
................. 91
Chapter
9
Discrete Valuation Rings and Dedekind Domains
..... 93
Discrete valuation rings
............ 94
Dedekind domains
.............. 95
Fractional ideals
.............. 96
Exercises
................. 99
Chapter
10
Completions
................ 100
Topologies and completions
........... 101
Filtrerions
................ 105
Graded rings and modules
............ 106
The associated graded ring
........... 1
И
Exercises
........... ..... 113
Chapter
11
Dimension Theory
..............
u6
Hubert functions
..............
U6
Dimension theory of Noetherian local rings
...... 119
Regular local rings
........■..... 123
Transcendental dimension
............ 124
Exercises
................. 125
Index.
................ . 127
|
| any_adam_object | 1 |
| author | Atiyah, Michael Francis 1929-2019 Macdonald, Ian G. 1928- |
| author_GND | (DE-588)118848453 (DE-588)123369258 |
| author_facet | Atiyah, Michael Francis 1929-2019 Macdonald, Ian G. 1928- |
| author_role | aut aut |
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| bvnumber | BV036097312 |
| classification_rvk | SK 230 |
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| discipline | Mathematik |
| edition | [reprint.] |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:11:31Z |
| institution | BVB |
| isbn | 0201407515 9780201407518 |
| language | Undetermined |
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| physical | 128 S. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
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| series2 | Addison-Wesley series in mathematics |
| spelling | Atiyah, Michael Francis 1929-2019 Verfasser (DE-588)118848453 aut Introduction to commutative algebra M. F. Atiyah ; I. G. MacDonald [reprint.] Reading, Mass. [u.a.] Addison-Wesley [2010] 128 S. txt rdacontent n rdamedia nc rdacarrier Addison-Wesley series in mathematics Ring Mathematik (DE-588)4128084-2 gnd rswk-swf Kommutative Algebra (DE-588)4164821-3 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Kommutative Algebra (DE-588)4164821-3 s Ring Mathematik (DE-588)4128084-2 s 2\p DE-604 Macdonald, Ian G. 1928- Verfasser (DE-588)123369258 aut Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018987780&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 | Atiyah, Michael Francis 1929-2019 Macdonald, Ian G. 1928- Introduction to commutative algebra Ring Mathematik (DE-588)4128084-2 gnd Kommutative Algebra (DE-588)4164821-3 gnd |
| subject_GND | (DE-588)4128084-2 (DE-588)4164821-3 (DE-588)4151278-9 |
| title | Introduction to commutative algebra |
| title_auth | Introduction to commutative algebra |
| title_exact_search | Introduction to commutative algebra |
| title_full | Introduction to commutative algebra M. F. Atiyah ; I. G. MacDonald |
| title_fullStr | Introduction to commutative algebra M. F. Atiyah ; I. G. MacDonald |
| title_full_unstemmed | Introduction to commutative algebra M. F. Atiyah ; I. G. MacDonald |
| title_short | Introduction to commutative algebra |
| title_sort | introduction to commutative algebra |
| topic | Ring Mathematik (DE-588)4128084-2 gnd Kommutative Algebra (DE-588)4164821-3 gnd |
| topic_facet | Ring Mathematik Kommutative Algebra Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018987780&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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