Introduction to commutative algebra:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Bouder, Colo. [u.a.]
Westview Press
[1994]
|
| Edition: | [reprint.] |
| Series: | Addison-Wesley series in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 128 S. |
| ISBN: | 0201407515 9780201407518 |
Staff View
MARC
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| 245 | 1 | 0 | |a Introduction to commutative algebra |c M. F. Atiyah ; I. G. MacDonald |
| 250 | |a [reprint.] | ||
| 264 | 1 | |a Bouder, Colo. [u.a.] |b Westview Press |c [1994] | |
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Record in the Search Index
| _version_ | 1804137512471363584 |
|---|---|
| adam_text | Contents
Introduction
................
vii
Notation
and
Terminology
............ ix
Chapter
1
Rings and
Ideais
............... 1
Rings and ring homomorphisms
.......... 1
Ideals.
Quotient
rings
............. 2
Zero-divisors.
Nilpotent
elements. Units
........ 2
Prime ideals and maximal ideals
.......... 3
Nilradical and
Jacobson
radical
. . . .......
S
Operations on ideals
............. 6
Extension and contraction
............ 9
Exercises
................ 10
Chapter! Modules
................. 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
scalare
......... 27
Exactness properties of the tensor product
....... 28
Algebras
.................. 29
Tensor product of algebras
........... 30
Exercises
................. 31
Chapters Rings and Modules of Fractions
.......... 36
Local properties
............... 40
Extended and contracted ideals in rings of fractions
.... 41
Exercises
................. 43
Chapter
4
Primary Decomposition
............ 50
Exercises
.................
SS
v
VÍ
CONTENTS
Chapter
5
Integral Dependence and Valuations
......... 59
Integral dependence
............. 59
The
going-up
theorem
............. 61
Integrally closed integral domains. The going-down theorem.
. 62
Valuation rings
............... 65
Exercises
................. 67
Chapter
б
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
Complétions
................ 100
Topologies and completions
........... 101
Filtrations
................ 105
Graded rings and modules
............106
The associated graded ring
...........
HI
Exercises
.................
ИЗ
Chapter
U
Dimension Theory
.............. 116
Hubert functions
..............
П6
Dimension theory of Noetherian local rings
...... 119
Regular local rings
.............. 123
Transcendental dimension
............ 124
Exercises
................. 125
Index
.................. 127
|
| adam_txt |
Contents
Introduction
.
vii
Notation
and
Terminology
. ix
Chapter
1
Rings and
Ideais
. 1
Rings and ring homomorphisms
. 1
Ideals.
Quotient
rings
. 2
Zero-divisors.
Nilpotent
elements. Units
. 2
Prime ideals and maximal ideals
. 3
Nilradical and
Jacobson
radical
. . .'.
S
Operations on ideals
. 6
Extension and contraction
. 9
Exercises
. 10
Chapter! Modules
. 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
scalare
. 27
Exactness properties of the tensor product
. 28
Algebras
. 29
Tensor product of algebras
. 30
Exercises
. 31
Chapters Rings and Modules of Fractions
. 36
Local properties
. 40
Extended and contracted ideals in rings of fractions
. 41
Exercises
. 43
Chapter
4
Primary Decomposition
. 50
Exercises
.
SS
v
VÍ
CONTENTS
Chapter
5
Integral Dependence and Valuations
. 59
Integral dependence
. 59
The
going-up
theorem
. 61
Integrally closed integral domains. The going-down theorem.
. 62
Valuation rings
. 65
Exercises
. 67
Chapter
б
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
Complétions
. 100
Topologies and completions
. 101
Filtrations
. 105
Graded rings and modules
.106
The associated graded ring
.
HI
Exercises
.
ИЗ
Chapter
U
Dimension Theory
. 116
Hubert functions
.
П6
Dimension theory of Noetherian local rings
. 119
Regular local rings
. 123
Transcendental dimension
. 124
Exercises
. 125
Index
. 127 |
| any_adam_object | 1 |
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| author | Atiyah, Michael Francis 1929-2019 Macdonald, Ian G. 1928- |
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| ctrlnum | (OCoLC)257972389 (DE-599)BVBBV023223718 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | [reprint.] |
| format | Book |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T20:17:05Z |
| indexdate | 2024-07-09T21:13:28Z |
| institution | BVB |
| isbn | 0201407515 9780201407518 |
| language | English |
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| physical | 128 S. |
| publishDate | 1994 |
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| publisher | Westview Press |
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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.] Bouder, Colo. [u.a.] Westview Press [1994] 128 S. txt rdacontent n rdamedia nc rdacarrier Addison-Wesley series in mathematics Kommutative Algebra (DE-588)4164821-3 gnd rswk-swf Ring Mathematik (DE-588)4128084-2 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 Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016409569&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 Kommutative Algebra (DE-588)4164821-3 gnd Ring Mathematik (DE-588)4128084-2 gnd |
| subject_GND | (DE-588)4164821-3 (DE-588)4128084-2 (DE-588)4151278-9 |
| title | Introduction to commutative algebra |
| title_auth | Introduction to commutative algebra |
| title_exact_search | Introduction to commutative algebra |
| title_exact_search_txtP | 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 | Kommutative Algebra (DE-588)4164821-3 gnd Ring Mathematik (DE-588)4128084-2 gnd |
| topic_facet | Kommutative Algebra Ring Mathematik Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016409569&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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