Cohen-Macaulay rings:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge u. a.
Cambridge Univ. Press
1998
|
| Ausgabe: | 1. paperback ed. with revisions |
| Schriftenreihe: | Cambridge studies in advanced mathematics
39 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 453 S. graph. Darst. |
| ISBN: | 0521566746 9780521566742 |
Internformat
MARC
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| 020 | |a 9780521566742 |9 978-0-521-56674-2 | ||
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| 084 | |a 13H10 |2 msc | ||
| 100 | 1 | |a Bruns, Winfried |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Cohen-Macaulay rings |c Winfried Bruns ; Jürgen Herzog |
| 250 | |a 1. paperback ed. with revisions | ||
| 264 | 1 | |a Cambridge u. a. |b Cambridge Univ. Press |c 1998 | |
| 300 | |a XIV, 453 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Cambridge studies in advanced mathematics |v 39 | |
| 650 | 0 | 7 | |a Cohen-Macaulay-Ring |0 (DE-588)4200397-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Cohen-Macaulay-Ring |0 (DE-588)4200397-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Herzog, Jürgen |d 1941-2024 |e Verfasser |0 (DE-588)142854115 |4 aut | |
| 830 | 0 | |a Cambridge studies in advanced mathematics |v 39 |w (DE-604)BV000003678 |9 39 | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-010281191 | |
Datensatz im Suchindex
| _version_ | 1808406147440312320 |
|---|---|
| adam_text |
Contents
Preface
to the revised edition
xi
Preface to the first edition
xii
I Basic concepts
1
1
Regular sequences and depth
3
1.1
Regular sequences
. 3
1.2
Grade and depth
. 8
1.3
Depth and
projective
dimension
. 16
1.4
Some linear algebra
. 18
1.5
Graded rings and modules
. 27
1.6
The
Koszul
complex
. 40
Notes
. 55
2
Cohen-Macaulay rings
57
2.1
Cohen-Macaulay rings and modules
. 57
2.2
Regular rings and normal rings
. 65
2.3
Complete intersections
. 73
Notes
. 85
3
The canonical module. Gorenstein rings
88
3.1
Finite modules of finite injective dimension
. 88
3.2
Injective hulls. Matlis duality
. 97
3.3
The canonical module
. 107
3.4
Gorenstein ideals of grade
3.
Poincaré
duality
. 120
3.5
Local cohomology. The local duality theorem
. 127
3.6
The canonical module of a graded ring
. 136
Notes
. 144
4
Hubert functions and multiplicities
147
4.1
Hubert functions over homogeneous rings
. 147
4.2
Macaulay's theorem on Hilbert functions
. 156
4.3
Gotzmann's regularity and persistence theorem
. 168
4.4
Hilbert functions over graded rings
. 173
4.5
Filtered rings
. 182
4.6
The Hilbert-Samuel function and reduction ideals
. 188
4.7
The multiplicity symbol
. 192
Notes
. 201
vu
viii Contents
II
Classes
of Cohen-Macaulay rings
205
5
Stanley—
Reisner
rings
207
5.1
Simplicial complexes
. 207
5.2
Polytopes
. 223
5.3
Local cohomology of Stanley-Reisner rings
. 229
5.4
The upper bound theorem
. 237
5.5
Betti
numbers of Stanley-Reisner rings
. 240
5.6
Gorenstein complexes
. 243
5.7
The canonical module of a Stanley-Reisner ring
. 246
Notes
. 254
6
Semigroup rings and invariant theory
256
6.1 Affine
semigroup rings
. 256
6.2
Local cohomology of
affine
semigroup rings
. 263
6.3
Normal semigroup rings
. 270
6.4
Invariants of tori and finite groups
. 278
6.5
Invariants of linearly reductive groups
. 292
Notes
. 298
7
Determinantal rings
300
7.1
Graded Hodge algebras
. 300
7.2
Straightening laws on posets of minors
. 306
7.3
Properties of determinantal rings
. 311
Notes
. 318
III Characteristic
ρ
methods
321
8
Big Cohen-Macaulay modules
323
8.1
The annihilators of local cohomology
. 323
8.2
The Frobenius functor
. 327
8.3
Modifications and non-degeneracy
. 331
8.4
Hochster's finiteness theorem
. 336
8.5
Balanced big Cohen-Macaulay modules
. 342
Notes
. 346
9
Homological theorems
348
9.1
Grade and acyclicity
. 348
9.2
Regular rings as direct summands
. 354
9.3
Canonical elements in local cohomology modules
. 357
9.4
Intersection theorems
. 361
9.5
Ranks of syzygies
. 367
9.6
Bass numbers
. 372
Notes
. 376
Contents ix
10
Tight closure
378
10.1
The tight closure of an ideal
. 378
10.2
The
Briançon-Skoda
theorem
. 387
10.3
F
-rational rings
. 393
10.4
Direct summands of regular rings
. 406
Notes
. 410
Appendix: A summary of dimension theory
412
References
420
Notation
439
Index
444 |
| any_adam_object | 1 |
| author | Bruns, Winfried Herzog, Jürgen 1941-2024 |
| author_GND | (DE-588)142854115 |
| author_facet | Bruns, Winfried Herzog, Jürgen 1941-2024 |
| author_role | aut aut |
| author_sort | Bruns, Winfried |
| author_variant | w b wb j h jh |
| building | Verbundindex |
| bvnumber | BV017033316 |
| classification_rvk | SK 230 |
| classification_tum | MAT 130f |
| ctrlnum | (OCoLC)264670178 (DE-599)BVBBV017033316 |
| dewey-full | 512.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.4 |
| dewey-search | 512.4 |
| dewey-sort | 3512.4 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. paperback ed. with revisions |
| format | Book |
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| id | DE-604.BV017033316 |
| illustrated | Illustrated |
| indexdate | 2024-08-26T00:01:36Z |
| institution | BVB |
| isbn | 0521566746 9780521566742 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010281191 |
| oclc_num | 264670178 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-634 DE-83 DE-384 DE-11 |
| owner_facet | DE-91G DE-BY-TUM DE-634 DE-83 DE-384 DE-11 |
| physical | XIV, 453 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge studies in advanced mathematics |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Bruns, Winfried Verfasser aut Cohen-Macaulay rings Winfried Bruns ; Jürgen Herzog 1. paperback ed. with revisions Cambridge u. a. Cambridge Univ. Press 1998 XIV, 453 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge studies in advanced mathematics 39 Cohen-Macaulay-Ring (DE-588)4200397-0 gnd rswk-swf Cohen-Macaulay-Ring (DE-588)4200397-0 s DE-604 Herzog, Jürgen 1941-2024 Verfasser (DE-588)142854115 aut Cambridge studies in advanced mathematics 39 (DE-604)BV000003678 39 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010281191&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bruns, Winfried Herzog, Jürgen 1941-2024 Cohen-Macaulay rings Cambridge studies in advanced mathematics Cohen-Macaulay-Ring (DE-588)4200397-0 gnd |
| subject_GND | (DE-588)4200397-0 |
| title | Cohen-Macaulay rings |
| title_auth | Cohen-Macaulay rings |
| title_exact_search | Cohen-Macaulay rings |
| title_full | Cohen-Macaulay rings Winfried Bruns ; Jürgen Herzog |
| title_fullStr | Cohen-Macaulay rings Winfried Bruns ; Jürgen Herzog |
| title_full_unstemmed | Cohen-Macaulay rings Winfried Bruns ; Jürgen Herzog |
| title_short | Cohen-Macaulay rings |
| title_sort | cohen macaulay rings |
| topic | Cohen-Macaulay-Ring (DE-588)4200397-0 gnd |
| topic_facet | Cohen-Macaulay-Ring |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010281191&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003678 |
| work_keys_str_mv | AT brunswinfried cohenmacaulayrings AT herzogjurgen cohenmacaulayrings |