Graded ring theory:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Amsterdam, [u.a]
North-Holland Publishing Company
1982
|
| Schriftenreihe: | North-Holland mathematical library
Volume 28 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | ix, 340 Seiten |
| ISBN: | 044486489X |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV000239152 | ||
| 003 | DE-604 | ||
| 005 | 20240828 | ||
| 007 | t | ||
| 008 | 870612s1982 |||| 00||| ger d | ||
| 020 | |a 044486489X |9 0-444-86489-X | ||
| 035 | |a (OCoLC)8709270 | ||
| 035 | |a (DE-599)BVBBV000239152 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a ger | |
| 049 | |a DE-12 |a DE-384 |a DE-703 |a DE-739 |a DE-355 |a DE-29T |a DE-19 |a DE-706 |a DE-83 |a DE-188 | ||
| 050 | 0 | |a QA251.4 | |
| 082 | 0 | |a 512/.4 |2 19 | |
| 084 | |a SK 230 |0 (DE-625)143225: |2 rvk | ||
| 084 | |a 16A03 |2 msc/1980 | ||
| 084 | |a 13Exx |2 msc/1980 | ||
| 100 | 1 | |a Năstăsescu, Constantin |d 1943- |0 (DE-588)1286232074 |4 aut | |
| 245 | 1 | 0 | |a Graded ring theory |c C. Nǎstǎsescu and F. van Oystaeyen |
| 264 | 1 | |a Amsterdam, [u.a] |b North-Holland Publishing Company |c 1982 | |
| 300 | |a ix, 340 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a North-Holland mathematical library |v Volume 28 | |
| 650 | 4 | |a Anneaux gradués | |
| 650 | 4 | |a Anneaux non commutatifs | |
| 650 | 4 | |a Graded rings | |
| 650 | 4 | |a Noncommutative rings | |
| 650 | 0 | 7 | |a Graduierter Ring |0 (DE-588)4158003-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Graduierter Ring |0 (DE-588)4158003-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Van Oystaeyen, Freddy |d 1947- |0 (DE-588)128792884 |4 aut | |
| 830 | 0 | |a North-Holland mathematical library |v Volume 28 |w (DE-604)BV000005206 |9 28 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000143576&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-000143576 | |
Datensatz im Suchindex
| _version_ | 1808678803925368832 |
|---|---|
| adam_text |
vii
CONTENTS
A. SOME GENERAL TECHNIQUES IN THE THEORY OF
GRADED RINGS
I. Graded Rings and Modules
1.1. Graded Rings and the Category of Graded Modules 1
1.2. Elementary Properties of Graded Modules 7
1.3. Strongly Graded Rings 15
1.4. Graded Division Rings 38
1.5. Graded Endomorphism Rings 43
1.6. Graded Rings of Fractions 49
1.7. Jacobson Radicals of Graded Rings 52
1.8. Almost Strongly Graded Rings 62
1.9. Exercises, Comments, References 71
I1. Some General Techniques
11.1. Gradation by Ordered Groups 78
11.2. Internal Homogenization 83
11.3. Chain Conditions for Graded Modules 86
11.4. Invertible Ideals. The Rees Ring and the
Generalized Rees Ring 92
11.5. Krull Dimension of Graded Rings 95
11.6. The Structure of Simple Objects in R gr 106
11.7. Primary Decomposition 114
11.8. External Homogenization. Homological
Dimension for Graded Rings 120
11.9. Torsion Theories over Graded Rings 130
11.10. Graded Rings and Modules of Quotients 141
11.11. Injective Modules, Prime Kernel Functors
and Localizations at Prime Ideals 150
viii Contents
B. COMMUTATIVE GRADED RINGS
I. Some Commutative Algebra Revisited
1.1. Graded Fields 155
1.2. Integral Extensions of Graded Rings 160
1.3. Graded Valuation Rings in Graded Fields 163
II. Arithmetically Graded Rings
11.1. Graded Krull Domains. Class Groups 171
11.2. Generalized Rees Rings and Gr Dedekind Rings 179
11.3. References, Comments, Exercises 193
III. Local Conditions for Noetherian Graded Rings
111.1. Injective Dimension of Graded Rings 198
111.2. Regular, Gorenstein and Cohen Macaulay Rings 207
111.3. Graded Rings and M sequences 212
C. STRUCTURE THEORY FOR GRADED RINGS OF TYPE Z
I. Non Commutative Graded Rings
1.1. Rings of Fractions and Goldie's Theorem 222
1.2. Graded Rings Satisfying Polynomial Identities 231
1.3. Fully Bounded Graded Rings 238
1.4. Birational Graded Algebras 248
1.5. Graded Von Neumann Regular Rings 258
1.6. Exercises, Comments, References 273
D. FILTERED RINGS AND MODULES
I. The Category of Filtered Modules 278
II. Complete Filtered Modules. The Completion Functor 283
III. Filtration and Associated Gradation 287
IV. Free and Finitely Generated Objects of R filt 293
V. The l adic Filtration 298
VI. The Functor HOMR( , ). Filt projective (injective) ¦
Modules 306
Contents ix
VII. Projective Modules and Homological Dimensions
of Rings 312
VIM. Weak (Flat) Dimension of Filtered Modules 317
IX. Exercises. Comments. References 323
Bibliography 328
Index 336 |
| any_adam_object | 1 |
| author | Năstăsescu, Constantin 1943- Van Oystaeyen, Freddy 1947- |
| author_GND | (DE-588)1286232074 (DE-588)128792884 |
| author_facet | Năstăsescu, Constantin 1943- Van Oystaeyen, Freddy 1947- |
| author_role | aut aut |
| author_sort | Năstăsescu, Constantin 1943- |
| author_variant | c n cn o f v of ofv |
| building | Verbundindex |
| bvnumber | BV000239152 |
| callnumber-first | Q - Science |
| callnumber-label | QA251 |
| callnumber-raw | QA251.4 |
| callnumber-search | QA251.4 |
| callnumber-sort | QA 3251.4 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 230 |
| ctrlnum | (OCoLC)8709270 (DE-599)BVBBV000239152 |
| 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 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000 cb4500</leader><controlfield tag="001">BV000239152</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20240828</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">870612s1982 |||| 00||| ger d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">044486489X</subfield><subfield code="9">0-444-86489-X</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)8709270</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV000239152</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">ger</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA251.4</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512/.4</subfield><subfield code="2">19</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 230</subfield><subfield code="0">(DE-625)143225:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">16A03</subfield><subfield code="2">msc/1980</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">13Exx</subfield><subfield code="2">msc/1980</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Năstăsescu, Constantin</subfield><subfield code="d">1943-</subfield><subfield code="0">(DE-588)1286232074</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Graded ring theory</subfield><subfield code="c">C. Nǎstǎsescu and F. van Oystaeyen</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Amsterdam, [u.a]</subfield><subfield code="b">North-Holland Publishing Company</subfield><subfield code="c">1982</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">ix, 340 Seiten</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">North-Holland mathematical library</subfield><subfield code="v">Volume 28</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Anneaux gradués</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Anneaux non commutatifs</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Graded rings</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Noncommutative rings</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Graduierter Ring</subfield><subfield code="0">(DE-588)4158003-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Graduierter Ring</subfield><subfield code="0">(DE-588)4158003-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Van Oystaeyen, Freddy</subfield><subfield code="d">1947-</subfield><subfield code="0">(DE-588)128792884</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">North-Holland mathematical library</subfield><subfield code="v">Volume 28</subfield><subfield code="w">(DE-604)BV000005206</subfield><subfield code="9">28</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000143576&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-000143576</subfield></datafield></record></collection> |
| id | DE-604.BV000239152 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-29T00:15:21Z |
| institution | BVB |
| isbn | 044486489X |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000143576 |
| oclc_num | 8709270 |
| open_access_boolean | |
| owner | DE-12 DE-384 DE-703 DE-739 DE-355 DE-BY-UBR DE-29T DE-19 DE-BY-UBM DE-706 DE-83 DE-188 |
| owner_facet | DE-12 DE-384 DE-703 DE-739 DE-355 DE-BY-UBR DE-29T DE-19 DE-BY-UBM DE-706 DE-83 DE-188 |
| physical | ix, 340 Seiten |
| psigel | TUB-nveb |
| publishDate | 1982 |
| publishDateSearch | 1982 |
| publishDateSort | 1982 |
| publisher | North-Holland Publishing Company |
| record_format | marc |
| series | North-Holland mathematical library |
| series2 | North-Holland mathematical library |
| spelling | Năstăsescu, Constantin 1943- (DE-588)1286232074 aut Graded ring theory C. Nǎstǎsescu and F. van Oystaeyen Amsterdam, [u.a] North-Holland Publishing Company 1982 ix, 340 Seiten txt rdacontent n rdamedia nc rdacarrier North-Holland mathematical library Volume 28 Anneaux gradués Anneaux non commutatifs Graded rings Noncommutative rings Graduierter Ring (DE-588)4158003-5 gnd rswk-swf Graduierter Ring (DE-588)4158003-5 s DE-604 Van Oystaeyen, Freddy 1947- (DE-588)128792884 aut North-Holland mathematical library Volume 28 (DE-604)BV000005206 28 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000143576&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Năstăsescu, Constantin 1943- Van Oystaeyen, Freddy 1947- Graded ring theory North-Holland mathematical library Anneaux gradués Anneaux non commutatifs Graded rings Noncommutative rings Graduierter Ring (DE-588)4158003-5 gnd |
| subject_GND | (DE-588)4158003-5 |
| title | Graded ring theory |
| title_auth | Graded ring theory |
| title_exact_search | Graded ring theory |
| title_full | Graded ring theory C. Nǎstǎsescu and F. van Oystaeyen |
| title_fullStr | Graded ring theory C. Nǎstǎsescu and F. van Oystaeyen |
| title_full_unstemmed | Graded ring theory C. Nǎstǎsescu and F. van Oystaeyen |
| title_short | Graded ring theory |
| title_sort | graded ring theory |
| topic | Anneaux gradués Anneaux non commutatifs Graded rings Noncommutative rings Graduierter Ring (DE-588)4158003-5 gnd |
| topic_facet | Anneaux gradués Anneaux non commutatifs Graded rings Noncommutative rings Graduierter Ring |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000143576&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005206 |
| work_keys_str_mv | AT nastasescuconstantin gradedringtheory AT vanoystaeyenfreddy gradedringtheory |