Monomial algebras:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Dekker
2001
|
| Schriftenreihe: | Pure and applied mathematics
238 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 455 S. |
| ISBN: | 0824705246 |
Internformat
MARC
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| 245 | 1 | 0 | |a Monomial algebras |c Rafael H. Villarreal |
| 264 | 1 | |a New York [u.a.] |b Dekker |c 2001 | |
| 300 | |a IX, 455 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 650 | 0 | 7 | |a Kommutative Algebra |0 (DE-588)4164821-3 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804128315839086592 |
|---|---|
| adam_text | Contents
Preface Hi
1 Commutative Algebra 1
1.1 Module theory 1
1.2 Graded modules 12
1.3 Cohen Macaulay modules 16
1.4 Normal rings 23
1.5 Koszul homology 28
2 Afflne and Graded Algebras 31
2.1 Noether normalizations 31
2.2 Cohen Macaulay graded algebras 35
2.3 Hilbert Nullstellensatz 45
2.4 Grobner bases 48
2.5 Minimal resolutions 58
3 Rees Algebras and Normality 65
3.1 Symmetric algebras 65
3.2 Rees algebras and syzygetic ideals 66
3.3 Complete and normal ideals 69
3.4 A criterion of Jiirgen Herzog 82
3.5 Jacobian criterion 89
4 Hilbert Series 97
4.1 Hilbert Serre s Theorem 97
4.2 a invariants and h vectors 106
4.3 Extremal algebras 110
4.4 Initial degrees of Gorenstein ideals 118
4.5 A symbolic study of Koszul homology 125
vii
viii Contents
5 Monomial Ideals and Stanley Reisner Rings 129
5.1 Primary decomposition 129
5.2 Simplicial complexes and homology 138
5.3 Face rings 142
5.4 Hilbert series of face rings 150
5.5 Upper bound conjectures 154
6 Edge Ideals 161
6.1 Graphs and ideals 161
6.2 Cohen Macaulay graphs 172
6.3 Trees 178
6.4 Bipartite graphs 182
6.5 Links of some edge ideals 185
6.6 First syzygy module of an edge ideal 188
6.7 Edge rings with linear resolutions 192
7 Monomial Subrings 201
7.1 Basic properties 201
7.2 Integral closure of subrings 209
7.3 Integral closure of monomial ideals 233
7.4 Normality of some Rees algebras 239
7.5 Ideals of mixed products 248
7.6 Degree bounds for some integral closures 259
7.7 Degree bounds in the square free case 261
7.8 Some lexicographical Grobner bases 276
8 Monomial Subrings of Graphs 281
8.1 The subring associated to a graph 282
8.2 Rees algebras of edge ideals 286
8.3 Incidence matrix of a graph 294
8.4 Circuits of a graph and Grobner bases 296
8.5 Edge subrings of bipartite planar graphs 303
8.6 Normality of bipartite graphs 311
8.7 The integral closure of an edge subring 315
8.8 The equations of the edge cone 325
9 Semigroup Rings of Complete Graphs 335
9.1 Monomial subrings of bipartite graphs 335
9.2 Monomial subrings of complete graphs 350
9.3 Noether normalizations of edge subrings 359
Contents ix
10 Monomial Curves 367
10.1 Defining equations of monomial curves 367
10.2 Symmetric semigroups 377
10.3 Ideals generated by critical binomials 385
10.4 An algorithm for critical binomials 399
11 Afflne Toric Varieties and Toric Ideals 403
11.1 Systems of binomials in toric ideals . 403
11.2 Affine toric varieties 409
11.3 Curves in positive characteristic 414
A Graph Diagrams 421
A.I Cohen Macaulay graphs . 421
A.2 Unmixed graphs 424
Bibliography 425
Notation 447
Index 449
|
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV013523476 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:47:18Z |
| institution | BVB |
| isbn | 0824705246 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009230645 |
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| owner_facet | DE-355 DE-BY-UBR |
| physical | IX, 455 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Dekker |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Villarreal, Rafael H. Verfasser aut Monomial algebras Rafael H. Villarreal New York [u.a.] Dekker 2001 IX, 455 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 238 Kommutative Algebra (DE-588)4164821-3 gnd rswk-swf Kommutative Algebra (DE-588)4164821-3 s DE-604 Pure and applied mathematics 238 (DE-604)BV000001885 238 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009230645&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Villarreal, Rafael H. Monomial algebras Pure and applied mathematics Kommutative Algebra (DE-588)4164821-3 gnd |
| subject_GND | (DE-588)4164821-3 |
| title | Monomial algebras |
| title_auth | Monomial algebras |
| title_exact_search | Monomial algebras |
| title_full | Monomial algebras Rafael H. Villarreal |
| title_fullStr | Monomial algebras Rafael H. Villarreal |
| title_full_unstemmed | Monomial algebras Rafael H. Villarreal |
| title_short | Monomial algebras |
| title_sort | monomial algebras |
| topic | Kommutative Algebra (DE-588)4164821-3 gnd |
| topic_facet | Kommutative Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009230645&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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