Flat covers of modules:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1996
|
| Series: | Lecture notes in mathematics
1634 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 161 S. |
| ISBN: | 3540616403 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV010951159 | ||
| 003 | DE-604 | ||
| 005 | 20080208 | ||
| 007 | t | ||
| 008 | 960909s1996 gw |||| 00||| eng d | ||
| 016 | 7 | |a 948183837 |2 DE-101 | |
| 020 | |a 3540616403 |c : DM 44.00 |9 3-540-61640-3 | ||
| 035 | |a (OCoLC)246275159 | ||
| 035 | |a (DE-599)BVBBV010951159 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c DE | ||
| 049 | |a DE-20 |a DE-12 |a DE-91G |a DE-824 |a DE-19 |a DE-706 |a DE-634 |a DE-83 |a DE-11 |a DE-188 | ||
| 050 | 0 | |a QA3 | |
| 082 | 0 | |a 510 |2 20 | |
| 082 | 0 | |a 512/.4 |2 20 | |
| 084 | |a SI 850 |0 (DE-625)143199: |2 rvk | ||
| 084 | |a SK 230 |0 (DE-625)143225: |2 rvk | ||
| 084 | |a MAT 162f |2 stub | ||
| 084 | |a 16D40 |2 msc | ||
| 084 | |a 13C11 |2 msc | ||
| 100 | 1 | |a Xu, Jinzhong |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Flat covers of modules |c Jinzhong Xu |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1996 | |
| 300 | |a X, 161 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1634 | |
| 650 | 7 | |a Modulen (wiskunde) |2 gtt | |
| 650 | 4 | |a Modules (Algèbre) | |
| 650 | 7 | |a Modules (algèbre) |2 ram | |
| 650 | 4 | |a Modules (Algebra) | |
| 650 | 0 | 7 | |a Überdeckung |0 (DE-588)4186550-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Modultheorie |0 (DE-588)4170336-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Einhüllende |0 (DE-588)4151321-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kommutativer Ring |0 (DE-588)4164825-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Überdeckung |g Mathematik |0 (DE-588)4186551-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Modul |0 (DE-588)4129770-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Modultheorie |0 (DE-588)4170336-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Modul |0 (DE-588)4129770-2 |D s |
| 689 | 1 | 1 | |a Überdeckung |0 (DE-588)4186550-9 |D s |
| 689 | 1 | 2 | |a Einhüllende |0 (DE-588)4151321-6 |D s |
| 689 | 1 | |5 DE-604 | |
| 689 | 2 | 0 | |a Kommutativer Ring |0 (DE-588)4164825-0 |D s |
| 689 | 2 | 1 | |a Überdeckung |0 (DE-588)4186550-9 |D s |
| 689 | 2 | |5 DE-604 | |
| 689 | 3 | 0 | |a Modul |0 (DE-588)4129770-2 |D s |
| 689 | 3 | 1 | |a Überdeckung |g Mathematik |0 (DE-588)4186551-0 |D s |
| 689 | 3 | |5 DE-604 | |
| 689 | 4 | 0 | |a Kommutativer Ring |0 (DE-588)4164825-0 |D s |
| 689 | 4 | 1 | |a Überdeckung |g Mathematik |0 (DE-588)4186551-0 |D s |
| 689 | 4 | |5 DE-604 | |
| 830 | 0 | |a Lecture notes in mathematics |v 1634 |w (DE-604)BV000676446 |9 1634 | |
| 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=007324876&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
Record in the Search Index
| _version_ | 1805082793986752512 |
|---|---|
| adam_text |
Contents
0 Introduction 1
1 Envelopes and Covers 5
1.1 Preliminaries 5
1.2 Envelopes and covers 10
1.3 Flat covers and torsion free coverings 16
1.4 Direct sums of covers and envelopes 20
2 Fundamental Theorems 27
2.1 Wakamutsu's Lemmas 27
2.2 Fundamental theorems 30
2.3 Applications 37
2.4 Injective covers 41
2.5 Flat envelopes and preenvelopes 48
3 Flat Covers and Cotorsion Envelopes 51
3.1 Flat covers in an exact sequence 51
3.2 Modules of finite injective dimension 58
3.3 Cotorsion modules 62
3.4 Cotorsion envelopes 66
3.5 Extensions of pure injective modules 73
3.6 Relative homological theory 75
4 Flat Covers over Commutative Rings 81
4.1 Cotorsion flat modules 81
4.2 Minimal pure injective resolutions of flat modules 89
4.3 Flat covers of cotorsion modules 93
4.4 Flat covers of Matlis reflexive modules 98
4.5 A theorem on Artinian rings 103
5 Applications in Commutative Rings 107
5.1 The Bass numbers of flat modules 108
X
5.2 The dual Bass numbers 117
5.3 Minimal flat resolutions of injective modules 124
5.4 Strongly cotorsion modules 129
5.5 Foxby duality 137
5.6 Gorenstein projective, injective modules 141
5.7 Gorenstein flat modules and covers 145
Bibliography 153
Index 158 |
| any_adam_object | 1 |
| author | Xu, Jinzhong |
| author_facet | Xu, Jinzhong |
| author_role | aut |
| author_sort | Xu, Jinzhong |
| author_variant | j x jx |
| building | Verbundindex |
| bvnumber | BV010951159 |
| callnumber-first | Q - Science |
| callnumber-label | QA3 |
| callnumber-raw | QA3 |
| callnumber-search | QA3 |
| callnumber-sort | QA 13 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 850 SK 230 |
| classification_tum | MAT 162f |
| ctrlnum | (OCoLC)246275159 (DE-599)BVBBV010951159 |
| dewey-full | 510 512/.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics 512 - Algebra |
| dewey-raw | 510 512/.4 |
| dewey-search | 510 512/.4 |
| dewey-sort | 3510 |
| 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">BV010951159</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20080208</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">960909s1996 gw |||| 00||| eng d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">948183837</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3540616403</subfield><subfield code="c">: DM 44.00</subfield><subfield code="9">3-540-61640-3</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)246275159</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV010951159</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">DE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-20</subfield><subfield code="a">DE-12</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA3</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">510</subfield><subfield code="2">20</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512/.4</subfield><subfield code="2">20</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SI 850</subfield><subfield code="0">(DE-625)143199:</subfield><subfield code="2">rvk</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">MAT 162f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">16D40</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">13C11</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Xu, Jinzhong</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Flat covers of modules</subfield><subfield code="c">Jinzhong Xu</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">1996</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">X, 161 S.</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">Lecture notes in mathematics</subfield><subfield code="v">1634</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Modulen (wiskunde)</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Modules (Algèbre)</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Modules (algèbre)</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Modules (Algebra)</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Überdeckung</subfield><subfield code="0">(DE-588)4186550-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Modultheorie</subfield><subfield code="0">(DE-588)4170336-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Einhüllende</subfield><subfield code="0">(DE-588)4151321-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Kommutativer Ring</subfield><subfield code="0">(DE-588)4164825-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Überdeckung</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4186551-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Modul</subfield><subfield code="0">(DE-588)4129770-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Modultheorie</subfield><subfield code="0">(DE-588)4170336-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Modul</subfield><subfield code="0">(DE-588)4129770-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Überdeckung</subfield><subfield code="0">(DE-588)4186550-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="2"><subfield code="a">Einhüllende</subfield><subfield code="0">(DE-588)4151321-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">Kommutativer Ring</subfield><subfield code="0">(DE-588)4164825-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2="1"><subfield code="a">Überdeckung</subfield><subfield code="0">(DE-588)4186550-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="3" ind2="0"><subfield code="a">Modul</subfield><subfield code="0">(DE-588)4129770-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="3" ind2="1"><subfield code="a">Überdeckung</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4186551-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="3" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="4" ind2="0"><subfield code="a">Kommutativer Ring</subfield><subfield code="0">(DE-588)4164825-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="4" ind2="1"><subfield code="a">Überdeckung</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4186551-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="4" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Lecture notes in mathematics</subfield><subfield code="v">1634</subfield><subfield code="w">(DE-604)BV000676446</subfield><subfield code="9">1634</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=007324876&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield></record></collection> |
| id | DE-604.BV010951159 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-20T07:38:19Z |
| institution | BVB |
| isbn | 3540616403 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007324876 |
| oclc_num | 246275159 |
| open_access_boolean | |
| owner | DE-20 DE-12 DE-91G DE-BY-TUM DE-824 DE-19 DE-BY-UBM DE-706 DE-634 DE-83 DE-11 DE-188 |
| owner_facet | DE-20 DE-12 DE-91G DE-BY-TUM DE-824 DE-19 DE-BY-UBM DE-706 DE-634 DE-83 DE-11 DE-188 |
| physical | X, 161 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Xu, Jinzhong Verfasser aut Flat covers of modules Jinzhong Xu Berlin [u.a.] Springer 1996 X, 161 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1634 Modulen (wiskunde) gtt Modules (Algèbre) Modules (algèbre) ram Modules (Algebra) Überdeckung (DE-588)4186550-9 gnd rswk-swf Modultheorie (DE-588)4170336-4 gnd rswk-swf Einhüllende (DE-588)4151321-6 gnd rswk-swf Kommutativer Ring (DE-588)4164825-0 gnd rswk-swf Überdeckung Mathematik (DE-588)4186551-0 gnd rswk-swf Modul (DE-588)4129770-2 gnd rswk-swf Modultheorie (DE-588)4170336-4 s DE-604 Modul (DE-588)4129770-2 s Überdeckung (DE-588)4186550-9 s Einhüllende (DE-588)4151321-6 s Kommutativer Ring (DE-588)4164825-0 s Überdeckung Mathematik (DE-588)4186551-0 s Lecture notes in mathematics 1634 (DE-604)BV000676446 1634 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007324876&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Xu, Jinzhong Flat covers of modules Lecture notes in mathematics Modulen (wiskunde) gtt Modules (Algèbre) Modules (algèbre) ram Modules (Algebra) Überdeckung (DE-588)4186550-9 gnd Modultheorie (DE-588)4170336-4 gnd Einhüllende (DE-588)4151321-6 gnd Kommutativer Ring (DE-588)4164825-0 gnd Überdeckung Mathematik (DE-588)4186551-0 gnd Modul (DE-588)4129770-2 gnd |
| subject_GND | (DE-588)4186550-9 (DE-588)4170336-4 (DE-588)4151321-6 (DE-588)4164825-0 (DE-588)4186551-0 (DE-588)4129770-2 |
| title | Flat covers of modules |
| title_auth | Flat covers of modules |
| title_exact_search | Flat covers of modules |
| title_full | Flat covers of modules Jinzhong Xu |
| title_fullStr | Flat covers of modules Jinzhong Xu |
| title_full_unstemmed | Flat covers of modules Jinzhong Xu |
| title_short | Flat covers of modules |
| title_sort | flat covers of modules |
| topic | Modulen (wiskunde) gtt Modules (Algèbre) Modules (algèbre) ram Modules (Algebra) Überdeckung (DE-588)4186550-9 gnd Modultheorie (DE-588)4170336-4 gnd Einhüllende (DE-588)4151321-6 gnd Kommutativer Ring (DE-588)4164825-0 gnd Überdeckung Mathematik (DE-588)4186551-0 gnd Modul (DE-588)4129770-2 gnd |
| topic_facet | Modulen (wiskunde) Modules (Algèbre) Modules (algèbre) Modules (Algebra) Überdeckung Modultheorie Einhüllende Kommutativer Ring Überdeckung Mathematik Modul |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007324876&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT xujinzhong flatcoversofmodules |