Commutative algebra:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin ; Boston
De Gruyter
[2020]
|
| Schriftenreihe: | De Gruyter graduate
|
| Schlagwörter: | |
| Links: | http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110616972&searchTitles=true https://d-nb.info/1200036573/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032166468&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XV, 339 Seiten Illustrationen 24 cm |
| ISBN: | 9783110616972 |
Internformat
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| 245 | 1 | 0 | |a Commutative algebra |c Aron Simis |
| 264 | 1 | |a Berlin ; Boston |b De Gruyter |c [2020] | |
| 264 | 4 | |c © 2020 | |
| 300 | |a XV, 339 Seiten |b Illustrationen |c 24 cm | ||
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| 653 | |a Idealtheorie | ||
| 653 | |a Kommutative Algebra | ||
| 653 | |a Ringtheorie | ||
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| 689 | 0 | 0 | |a Kommutative Algebra |0 (DE-588)4164821-3 |D s |
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Datensatz im Suchindex
| _version_ | 1819362903830036480 |
|---|---|
| adam_text | CONTENTS
THANKS
*
V
FOREWORD
*
VII
PARTI
1
1.1
1.1.1
1.1.2
1.1.3
1.1.4
1.1.5
1.2
1.2.1
1.2.2
1.2.3
1.3
1.3.1
1.3.2
1.4
BASIC
INTRODUCTORY
THEORY
*
3
COMMUTATIVE
RINGS
AND
IDEALS
*
3
IDEALS,
GENERATORS
*
3
IDEALS,
RESIDUE
CLASSES
*
4
IDEAL
OPERATIONS
*
5
PRIME
AND
PRIMARY
IDEALS
*
8
A
SOURCE
OF
EXAMPLES:
MONOMIAL
IDEALS
*
9
ALGEBRAS
*
11
POLYNOMIALS
AND
FINITELY
GENERATED
ALGEBRAS
*
11
THE
TRANSCENDENCE
DEGREE
*
12
BASIC
PROPERTIES
OF
THE
TRANSCENDENCE
DEGREE
*
15
HISTORIC
NOTE
-----
17
TERMINOLOGY
-----
17
EARLY
ROOTS
*
17
EXERCISES
*
19
2
2.1
2.1.1
2.1.2
2.1.3
2.2
2.2.1
2.2.2
2.2.3
2.3
2.3.1
2.3.2
2.3.3
2.4
2.5
2.5.1
2.5.2
MAIN
TOOLS
*
23
RINGS
OF
FRACTIONS
----
23
DEFINITIONS
-----
23
GENERAL
PROPERTIES
OF
FRACTIONS
*
24
LOCAL
RINGS
AND
SYMBOLIC
POWERS
*
27
INTEGRAL
RING
EXTENSIONS
*
28
PRELIMINARIES
*
28
THE
COHEN-SEIDENBERG
THEOREMS
*
30
INTEGRAL
CLOSURE
OF
IDEALS
*
32
KRULL
DIMENSION
AND
NOETHER
NORMALIZATION
*
35
BEHAVIOR
IN
INTEGRAL
EXTENSIONS
*
36
NOETHER
NORMALIZATION
AND
THE
DIMENSION
THEOREM
*
36
COMPLEMENTS
TO
NOETHER
*
S
THEOREM
*
37
NULLSTELLENSATZ
*
38
DIMENSION
THEORY
1
-----42
NOETHERIAN
AND
ARTINIAN
RINGS
*
42
ASSOCIATED
PRIMES
*
50
XII
CONTENTS
2.5.3
2.5.4
2.6
2.6.1
2.6.2
2.7
2.7.1
2.7.2
2.7.3
2.7.4
2.7.5
2.8
2.8.1
2.8.2
2.8.3
2.8.4
2.8.5
2.8.6
2.8.7
2.9
KRULL
*
S
PRINCIPAL
IDEAL
THEOREM
*
53
DIMENSION
UNDER
EXTENSIONS
*
55
PRIMARY
DECOMPOSITION
*
60
THE
NATURE
OF
THE
COMPONENTS
*
60
THE
LASKER-NOETHER
FUNDAMENTAL
THEOREM
*
61
HILBERT
CHARACTERISTIC
FUNCTION
*
62
BASICS
ON
THE
UNDERLYING
GRADED
STRUCTURES
*
62
FIRST
RESULTS
-----67
MORE
ADVANCED
STEPS
*
68
THE
FORMULA
OF
VAN
DER
WAERDEN
*
74
MULTIPLICITIES
GALORE
*
77
HISTORIC
NOTE
-----
82
FRACTIONS
-----82
PRUFER
AND
THE
DETERMINANTS
TRICK
*
83
NOETHER
AND
KRULL
-----
84
PRIMARY
DECOMPOSITION
*
85
HILBERT
AND
ARTIN
-----
86
THE
LASKER-NOETHER
BINARY
-----
87
HILBERT
FUNCTION
-----89
EXERCISES
*
90
3
3.1
3.1.1
3.1.2
3.2
3.3
3.4
3.5
3.5.1
3.5.2
3.6
OVERVIEW
OF
MODULE
THEORY
*
99
NOETHERIAN
MODULES
*
99
CHAIN
CONDITIONS
*
99
COMPOSITION
SERIES
*
100
EXTERNAL
OPERATIONS
*
102
FREE
PRESENTATION
AND
FITTING
IDEALS
*
106
TORSION
AND
TORSION-FREE
MODULES
*
111
HISTORIC
NOTE
-----
114
COMPOSITION
SERIES
*
114
FITTING
IDEALS
-----
115
EXERCISES
*
115
4
4.1
4.1.1
4.1.2
4.2
4.2.1
4.2.2
4.2.3
4.2.4
DERIVATIONS,
DIFFERENTIALS
AND
JACOBIAN
IDEALS
*
119
PRELIMINARIES
*
119
DERIVATIONS
OF
SUBALGEBRAS
*
122
DERIVATIONS
WITH
VALUES
ON
A
LARGER
RING
*
124
DIFFERENTIAL
STRUCTURES
*
125
A
FIRST
STRUCTURE
THEOREM
*
125
THE
UNIVERSAL
MODULE
OF
DIFFERENTIALS
*
126
THE
CONORMAL
EXACT
SEQUENCE
*
127
KAHLER
DIFFERENTIALS
*
130
CONTENTS
*
XIII
4.3
4.3.1
4.3.2
4.4
4.4.1
4.4.2
4.5
4.6
THE
ISSUE
OF
REGULARITY
IN
ALGEBRA
AND
GEOMETRY
*
131
THE
JACOBIAN
IDEAL
*
131
HYPERSURFACES
*
132
DIFFERENTS
AND
RAMIFICATION
*
134
RAMIFICATION
-----
134
PURITY
-----
136
HISTORIC
NOTE
-----
137
EXERCISES
-----
138
PART
II
5
5.1
5.1.1
5.1.2
5.1.3
5.2
5.2.1
5.2.2
5.2.3
5.3
5.3.1
5.3.2
5.4
5.4.1
5.4.2
5.5
5.5.1
5.5.2
5.5.3
5.5.4
5.6
BASIC
ADVANCED
THEORY
*
145
DIMENSION
THEORY
*
145
ANNIHILATORS,
1
-----
145
THE
NAKAYAMA
LEMMA
*
145
THE
KRULL
DIMENSION
AND
SYSTEMS
OF
PARAMETERS
*
147
ASSOCIATED
PRIMES
AND
PRIMARY
DECOMPOSITION
*
151
ANNIHILATORS,
2
-----
151
ASSOCIATED
PRIMES
*
152
PRIMARY
DECOMPOSITION
-----
155
DEPTH
AND
COHEN-MACAULAY
MODULES
*
159
BASIC
PROPERTIES
OF
DEPTH
*
162
MOBILITY
OF
DEPTH
-----
164
COHEN-MACAULAY
MODULES
*
167
SPECIAL
PROPERTIES
OF
COHEN-MACAULAY
MODULES
*
169
NUMERICAL
INVARIANTS:
GORENSTEIN
RINGS
*
170
HISTORIC
NOTE
-----
174
DIMENSION
-----
174
PRIMARY
DECOMPOSITION
*
174
THE
DEPTH
BEHIND
THE
CURTAINS
-----
175
THE
KRUCHESAM
THEOREM
-----
175
EXERCISES
*
176
6
6.1
6.1.1
6.1.2
6.2
6.2.1
6.2.2
6.2.3
HOMOLOGICAL
METHODS
*
179
REGULAR
LOCAL
RINGS
-----
179
RELATION
TO
BASIC
INVARIANTS
*
179
PROPERTIES
*
181
THE
HOMOLOGICAL
TOOL
FOR
NOETHERIAN
RINGS
-----
182
PROJECTIVE
MODULES
*
182
HOMOLPGICAL
DIMENSION
-----
184
CHAIN
COMPLEXES
-----
200
XIV
*
CONTENTS
6.2.4
BASICS
ON
DERIVED
FUNCTORS
*
206
6.2.5
REES
THEOREM
AND
PERFECT
IDEALS
*
222
6.3
THE
METHOD
OF
THE
KOSZUL
COMPLEX
*
226
6.3.1
LONG
EXACT
SEQUENCES
OF
KOSZUL
HOMOLOGY
*
229
6.3.2
THE
THEOREM
OF
SERRE
*
234
6.4
VARIATIONS
ON
THE
KOSZUL
COMPLEX:
DETERMINANTAL
IDEALS
*
236
6.4.1
THE
EAGON-NORTHCOTT
COMPLEX
-----
236
6.4.2
THE
SCANDINAVIAN
COMPLEX
*
242
6.4.3
THE
JAPANESE-POLISH
COMPLEX
*
244
6.4.4
THE
OSNABRUCK-RECIFE
COMPLEX
*
246
6.5
HISTORIC
NOTE
-----
248
6.5.1
PROJECTIVE
MODULES
*
248
6.5.2
HOMOLOGY
-----
249
6.5.3
INJECTIVE
MODULES
*
249
6.5.4
DETERMINANTAL
IDEALS
*
250
6.6
EXERCISES
-----
251
7
GRADED
STRUCTURES
*
255
7.1
GRADED
PRELIMINARIES
*
255
7.2
THE
SYMMETRIC
ALGEBRA
*
257
7.2.1
TORSION-FREENESS
-----
258
7.2.2
IDEALS
OF
LINEAR
TYPE,
I
*
261
7.2.3
DIMENSION
-----
263
7.3
REES
ALGEBRAS
*
269
7.3.1
GEOMETRIC
ROOTS
*
269
7.3.2
DIMENSIONS
-----
271
7.3.3
THE
FIBER
CONE
AND
THE
ANALYTIC
SPREAD
*
276
7.3.4
IDEALS
OF
LINEAR
TYPE,
II
*
279
7.3.5
SPECIAL
PROPERTIES
(SURVEY)
-----
284
7.3.6
SPECIALIZATION
-----
289
7.4
HILBERT
FUNCTION
OF
MODULES
*
293
7.4.1
COMBINATORIAL
PRELIMINARIES
*
294
7.4.2
THE
GRADED
HILBERT
FUNCTION
----
297
7.4.3
INTERTWINING
GRADED
HILBERT
FUNCTIONS
*
303
7.4.4
THE
LOCAL
HILBERT-SAMUEL
FUNCTION
*
309
7.5
HISTORIC
NOTE
-----
316
7.5.1
THE
REES
ALGEBRA
*
316
7.5.2
THE
SYMMETRIC
ALGEBRA
*
316
7.5.3
ARTIN-REES
LEMMA
*
317
7.5.4
ASSOCIATIVITY
FORMULAS
*
317
7.6
EXERCISES
*
317
BIBLIOGRAPHY
*
321
INDEX
*
329
CONTENTS
*
XV
|
| any_adam_object | 1 |
| author | Simis, Aron 1942- |
| author_GND | (DE-588)120670683X |
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| ctrlnum | (OCoLC)1129049920 (DE-599)DNB1200036573 |
| dewey-full | 512.44 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.44 |
| dewey-search | 512.44 |
| dewey-sort | 3512.44 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV046756845 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T19:00:03Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783110616972 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032166468 |
| oclc_num | 1129049920 |
| open_access_boolean | |
| owner | DE-634 DE-83 DE-703 DE-20 DE-11 |
| owner_facet | DE-634 DE-83 DE-703 DE-20 DE-11 |
| physical | XV, 339 Seiten Illustrationen 24 cm |
| publishDate | 2020 |
| publishDateSearch | 2020 |
| publishDateSort | 2020 |
| publisher | De Gruyter |
| record_format | marc |
| series2 | De Gruyter graduate |
| spellingShingle | Simis, Aron 1942- Commutative algebra Kommutative Algebra (DE-588)4164821-3 gnd |
| subject_GND | (DE-588)4164821-3 |
| title | Commutative algebra |
| title_auth | Commutative algebra |
| title_exact_search | Commutative algebra |
| title_full | Commutative algebra Aron Simis |
| title_fullStr | Commutative algebra Aron Simis |
| title_full_unstemmed | Commutative algebra Aron Simis |
| title_short | Commutative algebra |
| title_sort | commutative algebra |
| topic | Kommutative Algebra (DE-588)4164821-3 gnd |
| topic_facet | Kommutative Algebra |
| url | http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110616972&searchTitles=true https://d-nb.info/1200036573/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032166468&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT simisaron commutativealgebra AT walterdegruytergmbhcokg commutativealgebra |