Graded and filtered rings and modules:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1979
|
| Schriftenreihe: | Lecture notes in mathematics
758 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 148 S. |
| ISBN: | 3540097082 0387097082 |
Internformat
MARC
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| 100 | 1 | |a Năstăsescu, Constantin |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Graded and filtered rings and modules |c C. Nǎstǎsescu ; F. Van Oystaeyen |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1979 | |
| 300 | |a X, 148 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 758 | |
| 650 | 4 | |a Anneaux associatifs | |
| 650 | 4 | |a Anneaux filtrés | |
| 650 | 4 | |a Anneaux gradués | |
| 650 | 4 | |a Modules filtrés | |
| 650 | 4 | |a Modules gradués | |
| 650 | 4 | |a Associative rings | |
| 650 | 4 | |a Filtered modules | |
| 650 | 4 | |a Filtered rings | |
| 650 | 4 | |a Graded modules | |
| 650 | 4 | |a Graded rings | |
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Datensatz im Suchindex
| _version_ | 1804116702056677376 |
|---|---|
| adam_text | CONTENTS
I. FILTERED RINGS AND MODULES 1
1.1. Preliminaries 1
1.2. The Category of Filtered ttodules 2
2.1. Remarks 3
2.2. Functors on R-filt. 3
1.3. Graded Rings and Modules 5
3.1. Examples 5
3.2. The Category of Graded Modules 5
3.3. Some Properties of Graded Modules 7
3.4. Tensor Product of Graded Modules 12
1.4. Filtration and Associated Gradation 13
1.5. Free, Projective and Finitely Generated Objects of R-filt 16
1.6. The Functor HO^ (.-,-). A
1.7. Projective Modules and Homological Dimension of Rings. 27
1.8. Weak (Flat) Dimension of Filtered Modules. 30
II. TOPICS IN GRADED RING THEORY 36
11.1. Homogenization 36
11.2. The Structure of Principal Graded Rings 38
11.3. Noetherian Objects 41
11.4. Krull Dimension of Graded Rings 47
11.5. The Krull Dimension of Some Classes of Rings 53
5.1. Polynomial Rings 53
5.2. Rings of Formal Power Series 55
5.3. The Enveloping Algebra of a Lie Algebra 56
5.4. Weyl Algebras 56
11.6. Graded Division Rings 58
11.7. The Structure of Simple Objects in R-gr. 59
11.8. The Jacobson Radical of Graded Rings. 65
11.9. Semisimple Graded Rings. Goldie s Theorems for Graded Rings 67
9.1. Graded Matrix Rings 67
9.2. Rings of Fractions and Goldie s Theorems 70
11.10. Primary Decompositions 74
11.11. External Homogenization 78
11.12. Graded Rings and Modules of Quotients 83
12.1. Torsion Theories over Graded Rings 83
12.2. Examples of Torsion Theories in R-gr. 89
12.3. Injective Objects and Torsion Theories 91
VIII
12.4. Graded Rings and Modules of Quotients 95
12.5. More Properties of Graded Localization 100
11.13. Graded Prime Ideals and the Ore Condition 107
11.14. The Presheaves on Proj R. 110
II. 15. Graded Zariski Central Rings 116
15.1. Basic Facts about Zariski Central Rings 116
15.2. GZ- and ZG-Rings 118
11.16. Scheme Structure of Proj over a Graded Zariski Central Ring 121
III. LOCAL CONDITIONS FOR NOETHERIAN GRADED RINGS 127
III. 1. Injective Dimension of Graded Rings 127
111.2. Regular, Gorenstein and Cohen-Macaulay Rings 133
111.3. Graded Rings and M-sequences. 137
REFERENCES 144
SUBJECT INDEX 146
|
| any_adam_object | 1 |
| author | Năstăsescu, Constantin Van Oystaeyen, Freddy 1947- |
| author_GND | (DE-588)128792884 |
| author_facet | Năstăsescu, Constantin Van Oystaeyen, Freddy 1947- |
| author_role | aut aut |
| author_sort | Năstăsescu, Constantin |
| author_variant | c n cn o f v of ofv |
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| bvnumber | BV002245934 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 850 SK 230 |
| ctrlnum | (OCoLC)5677956 (DE-599)BVBBV002245934 |
| dewey-full | 512/.4 510/.8 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV002245934 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:42:42Z |
| institution | BVB |
| isbn | 3540097082 0387097082 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001475979 |
| oclc_num | 5677956 |
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| physical | X, 148 S. |
| publishDate | 1979 |
| publishDateSearch | 1979 |
| publishDateSort | 1979 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Năstăsescu, Constantin Verfasser aut Graded and filtered rings and modules C. Nǎstǎsescu ; F. Van Oystaeyen Berlin [u.a.] Springer 1979 X, 148 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 758 Anneaux associatifs Anneaux filtrés Anneaux gradués Modules filtrés Modules gradués Associative rings Filtered modules Filtered rings Graded modules Graded rings Graduierter Modul (DE-588)4158002-3 gnd rswk-swf Filtrierter Modul (DE-588)4154395-6 gnd rswk-swf Filtrierter Ring (DE-588)4154396-8 gnd rswk-swf Graduierter Ring (DE-588)4158003-5 gnd rswk-swf Filtrierter Modul (DE-588)4154395-6 s DE-604 Filtrierter Ring (DE-588)4154396-8 s Graduierter Modul (DE-588)4158002-3 s Graduierter Ring (DE-588)4158003-5 s Van Oystaeyen, Freddy 1947- Verfasser (DE-588)128792884 aut Lecture notes in mathematics 758 (DE-604)BV000676446 758 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001475979&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Năstăsescu, Constantin Van Oystaeyen, Freddy 1947- Graded and filtered rings and modules Lecture notes in mathematics Anneaux associatifs Anneaux filtrés Anneaux gradués Modules filtrés Modules gradués Associative rings Filtered modules Filtered rings Graded modules Graded rings Graduierter Modul (DE-588)4158002-3 gnd Filtrierter Modul (DE-588)4154395-6 gnd Filtrierter Ring (DE-588)4154396-8 gnd Graduierter Ring (DE-588)4158003-5 gnd |
| subject_GND | (DE-588)4158002-3 (DE-588)4154395-6 (DE-588)4154396-8 (DE-588)4158003-5 |
| title | Graded and filtered rings and modules |
| title_auth | Graded and filtered rings and modules |
| title_exact_search | Graded and filtered rings and modules |
| title_full | Graded and filtered rings and modules C. Nǎstǎsescu ; F. Van Oystaeyen |
| title_fullStr | Graded and filtered rings and modules C. Nǎstǎsescu ; F. Van Oystaeyen |
| title_full_unstemmed | Graded and filtered rings and modules C. Nǎstǎsescu ; F. Van Oystaeyen |
| title_short | Graded and filtered rings and modules |
| title_sort | graded and filtered rings and modules |
| topic | Anneaux associatifs Anneaux filtrés Anneaux gradués Modules filtrés Modules gradués Associative rings Filtered modules Filtered rings Graded modules Graded rings Graduierter Modul (DE-588)4158002-3 gnd Filtrierter Modul (DE-588)4154395-6 gnd Filtrierter Ring (DE-588)4154396-8 gnd Graduierter Ring (DE-588)4158003-5 gnd |
| topic_facet | Anneaux associatifs Anneaux filtrés Anneaux gradués Modules filtrés Modules gradués Associative rings Filtered modules Filtered rings Graded modules Graded rings Graduierter Modul Filtrierter Modul Filtrierter Ring Graduierter Ring |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001475979&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT nastasescuconstantin gradedandfilteredringsandmodules AT vanoystaeyenfreddy gradedandfilteredringsandmodules |