Classes of modules:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton, FL [u.a.]
Chapman & Hall/CRC
2006
|
| Schriftenreihe: | Pure and applied mathematics
[281] |
| Schlagworte: | |
| Online-Zugang: | Table of contents only Publisher description Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 205 - 213 |
| Beschreibung: | X, 218 S. |
| ISBN: | 1584886609 9781584886600 |
Internformat
MARC
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| 650 | 4 | |a Ensembles, Théorie des | |
| 650 | 4 | |a Modules (Algèbre) | |
| 650 | 4 | |a Set theory | |
| 650 | 4 | |a Modules (Algebra) | |
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Datensatz im Suchindex
| _version_ | 1804137267100385280 |
|---|---|
| adam_text | Contents
Preface v
Note to the Reader vii
List of Symbols ix
Chapter I. Preliminary Background 1
1.1. Notation and Terminology 1
1.2. Lattices 5
Chapter 2. Important Module Classes and Constructions 7
2.1. Torsion Theory 7
2.2. Module Class a[M] 12
2.3. Natural Classes 19
2.4. M-Natural Classes 24
2.5. Pre-Natural Classes 29
Chapter 3. Finiteness Conditions 33
3.1. Ascending Chain Conditions 33
3.2. Descending Chain Conditions 50
3.3. Covers and Ascending Chain Conditions 65
Chapter 4. Type Theory of Modules: Dimension 71
4.1. Type Submodules and Type Dimensions 71
4.2. Several Type Dimension Formulas 80
4.3. Some Non-Classical Finiteness Conditions 87
IV
Chapter 5. Type Theory of Modules: Decompositions 107
5.1. Type Direct Sum Decompositions 108
5.2. Decomposability of Modules 117
5.3. Unique Type Closure Modules 132
5.4. TS-Modules 142
Chapter 6. Lattices of Module Classes 149
6.1. Lattice of Pre-Natural Classes 149
6.2. More Sublattice Structures 153
6.3. Lattice Properties of N?{R) 163
6.4. More Lattice Properties of N?{R) 177
6.5. Lattice Afr(R) and Its Applications 190
6.6. Boolean Ideal Lattice 200
References 205
Index 215
|
| adam_txt |
Contents
Preface v
Note to the Reader vii
List of Symbols ix
Chapter I. Preliminary Background 1
1.1. Notation and Terminology 1
1.2. Lattices 5
Chapter 2. Important Module Classes and Constructions 7
2.1. Torsion Theory 7
2.2. Module Class a[M] 12
2.3. Natural Classes 19
2.4. M-Natural Classes 24
2.5. Pre-Natural Classes 29
Chapter 3. Finiteness Conditions 33
3.1. Ascending Chain Conditions 33
3.2. Descending Chain Conditions 50
3.3. Covers and Ascending Chain Conditions 65
Chapter 4. Type Theory of Modules: Dimension 71
4.1. Type Submodules and Type Dimensions 71
4.2. Several Type Dimension Formulas 80
4.3. Some Non-Classical Finiteness Conditions 87
IV
Chapter 5. Type Theory of Modules: Decompositions 107
5.1. Type Direct Sum Decompositions 108
5.2. Decomposability of Modules 117
5.3. Unique Type Closure Modules 132
5.4. TS-Modules 142
Chapter 6. Lattices of Module Classes 149
6.1. Lattice of Pre-Natural Classes 149
6.2. More Sublattice Structures 153
6.3. Lattice Properties of N?{R) 163
6.4. More Lattice Properties of N?{R) 177
6.5. Lattice Afr(R) and Its Applications 190
6.6. Boolean Ideal Lattice 200
References 205
Index 215 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Dauns, John Zhou, Yiqiang |
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| ctrlnum | (OCoLC)66527318 (DE-599)BVBBV023038879 |
| dewey-full | 512/.42 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.42 |
| dewey-search | 512/.42 |
| dewey-sort | 3512 242 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T19:19:55Z |
| indexdate | 2024-07-09T21:09:34Z |
| institution | BVB |
| isbn | 1584886609 9781584886600 |
| language | English |
| lccn | 2006045438 |
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| physical | X, 218 S. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Chapman & Hall/CRC |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics Monographs and textsbooks in pure and applied mathematics |
| spelling | Dauns, John Verfasser aut Classes of modules John Dauns ; Yiqiang Zhou Boca Raton, FL [u.a.] Chapman & Hall/CRC 2006 X, 218 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics [281] Monographs and textsbooks in pure and applied mathematics Literaturverz. S. 205 - 213 Anneaux (Algèbre) Ensembles, Théorie des Modules (Algèbre) Set theory Modules (Algebra) Rings (Algebra) Modultheorie (DE-588)4170336-4 gnd rswk-swf Ringtheorie (DE-588)4126571-3 gnd rswk-swf Modultheorie (DE-588)4170336-4 s Ringtheorie (DE-588)4126571-3 s DE-604 Zhou, Yiqiang Verfasser aut Pure and applied mathematics [281] (DE-604)BV000001885 281 http://www.loc.gov/catdir/toc/fy0702/2006045438.html Table of contents only http://www.loc.gov/catdir/enhancements/fy0654/2006045438-d.html Publisher description HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016242547&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dauns, John Zhou, Yiqiang Classes of modules Pure and applied mathematics Anneaux (Algèbre) Ensembles, Théorie des Modules (Algèbre) Set theory Modules (Algebra) Rings (Algebra) Modultheorie (DE-588)4170336-4 gnd Ringtheorie (DE-588)4126571-3 gnd |
| subject_GND | (DE-588)4170336-4 (DE-588)4126571-3 |
| title | Classes of modules |
| title_auth | Classes of modules |
| title_exact_search | Classes of modules |
| title_exact_search_txtP | Classes of modules |
| title_full | Classes of modules John Dauns ; Yiqiang Zhou |
| title_fullStr | Classes of modules John Dauns ; Yiqiang Zhou |
| title_full_unstemmed | Classes of modules John Dauns ; Yiqiang Zhou |
| title_short | Classes of modules |
| title_sort | classes of modules |
| topic | Anneaux (Algèbre) Ensembles, Théorie des Modules (Algèbre) Set theory Modules (Algebra) Rings (Algebra) Modultheorie (DE-588)4170336-4 gnd Ringtheorie (DE-588)4126571-3 gnd |
| topic_facet | Anneaux (Algèbre) Ensembles, Théorie des Modules (Algèbre) Set theory Modules (Algebra) Rings (Algebra) Modultheorie Ringtheorie |
| url | http://www.loc.gov/catdir/toc/fy0702/2006045438.html http://www.loc.gov/catdir/enhancements/fy0654/2006045438-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016242547&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001885 |
| work_keys_str_mv | AT daunsjohn classesofmodules AT zhouyiqiang classesofmodules |