Continuous and discrete modules /:
Continuous and discrete modules are, essentially, generalizations of infective and projective modules respectively. Continuous modules provide an appropriate setting for decomposition theory of von Neumann algebras and have important applications to C*-algebras. Discrete modules constitute a dual co...
Gespeichert in:
| 1. Verfasser: | |
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| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York :
Cambridge University Press,
1990.
|
| Schriftenreihe: | London Mathematical Society lecture note series ;
147. |
| Schlagworte: | |
| Online-Zugang: | DE-862 DE-863 |
| Zusammenfassung: | Continuous and discrete modules are, essentially, generalizations of infective and projective modules respectively. Continuous modules provide an appropriate setting for decomposition theory of von Neumann algebras and have important applications to C*-algebras. Discrete modules constitute a dual concept and are related to number theory and algebraic geometry: they possess perfect decomposition properties. The advantage of both types of module is that the Krull-Schmidt theorem can be applied, in part, to them. The authors present here a complete account of the subject and at the same time give a unified picture of the theory. The treatment is essentially self-contained, with background facts being summarized in the first chapter. This book will be useful therefore either to individuals beginning research, or the more experienced worker in algebra and representation theory. |
| Beschreibung: | 1 online resource (126 pages) |
| Bibliographie: | Includes bibliographical references (pages 108-121) and index. |
| ISBN: | 9781107361669 1107361664 9780511892523 0511892527 |
Internformat
MARC
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| 100 | 1 | |a Mohamed, Saad H. | |
| 245 | 1 | 0 | |a Continuous and discrete modules / |c Saad H. Mohamed, Bruno J. Müller. |
| 260 | |a Cambridge ; |a New York : |b Cambridge University Press, |c 1990. | ||
| 300 | |a 1 online resource (126 pages) | ||
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| 490 | 1 | |a London Mathematical Society lecture note series ; |v 147 | |
| 504 | |a Includes bibliographical references (pages 108-121) and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a Continuous and discrete modules are, essentially, generalizations of infective and projective modules respectively. Continuous modules provide an appropriate setting for decomposition theory of von Neumann algebras and have important applications to C*-algebras. Discrete modules constitute a dual concept and are related to number theory and algebraic geometry: they possess perfect decomposition properties. The advantage of both types of module is that the Krull-Schmidt theorem can be applied, in part, to them. The authors present here a complete account of the subject and at the same time give a unified picture of the theory. The treatment is essentially self-contained, with background facts being summarized in the first chapter. This book will be useful therefore either to individuals beginning research, or the more experienced worker in algebra and representation theory. | ||
| 505 | 0 | |a Cover; Title; Copyright; Preface; Contents; Chapter 1: Injectivity and related concepts; 1.A-injective modules; 2. Quasi-injective modules; 3. Exchange and cancellation properties; 4. Decomposition theorems; Comments; Chapter 2: Quasi-continuous modules; 1. Basic properties; 2. Direct sums of quasi-continuous modules; 3. Decompositions of quasi-continuous modules; 4. Internal cancellation property; 5. Quasi-continuity versus quasi-injectivity; Comments; Chapter 3: Continuous modules; 1. Endomorphism rings; 2. Continuous modules; 3. The exchange property; Comments; Chapter 4: Quasi-discrete modules | |
| 505 | 8 | |a 1. Definition and basic results2. Decomposition theorems; 3. Applications of the decomposition theorems; 4. Discreteness and projectivity; 5. Quasi-discreteness of direct sums; Comments; Chapter 5: Discrete modules; 1. Discrete modules; 2. Endomorphism rings; 3.Commutative noetherian rings; Comments; Appendix; 1. Variants of supplementation; 2. Supplements are summands; 3. Extending modules; 4. The historial origin of the concept of; 5.N -continuity; 6. Open questions; Bibliography; Notation; Index | |
| 650 | 0 | |a Injective modules (Algebra) |0 http://id.loc.gov/authorities/subjects/sh85066449 | |
| 650 | 0 | |a Projective modules (Algebra) |0 http://id.loc.gov/authorities/subjects/sh85107381 | |
| 650 | 0 | |a Representations of rings (Algebra) |0 http://id.loc.gov/authorities/subjects/sh85112945 | |
| 650 | 0 | |a Decomposition (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh85036222 | |
| 650 | 6 | |a Modules injectifs (Algèbre) | |
| 650 | 6 | |a Modules projectifs (Algèbre) | |
| 650 | 6 | |a Représentations d'anneaux (Algèbre) | |
| 650 | 6 | |a Décomposition (Mathématiques) | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x Intermediate. |2 bisacsh | |
| 650 | 7 | |a Decomposition (Mathematics) |2 fast | |
| 650 | 7 | |a Injective modules (Algebra) |2 fast | |
| 650 | 7 | |a Projective modules (Algebra) |2 fast | |
| 650 | 7 | |a Representations of rings (Algebra) |2 fast | |
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| 700 | 1 | |a Müller, Bruno J. | |
| 776 | 0 | 8 | |i Print version: |a Mohamed, Saad H. |t Continuous and discrete modules. |d Cambridge ; New York : Cambridge University Press, 1990 |z 0521399750 |w (DLC) 91168120 |w (OCoLC)21351057 |
| 830 | 0 | |a London Mathematical Society lecture note series ; |v 147. |0 http://id.loc.gov/authorities/names/n42015587 | |
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Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn839305296 |
|---|---|
| _version_ | 1829094955991171072 |
| adam_text | |
| any_adam_object | |
| author | Mohamed, Saad H. |
| author2 | Müller, Bruno J. |
| author2_role | |
| author2_variant | b j m bj bjm |
| author_facet | Mohamed, Saad H. Müller, Bruno J. |
| author_role | |
| author_sort | Mohamed, Saad H. |
| author_variant | s h m sh shm |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
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| callnumber-raw | QA247 .M615 1990eb |
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| contents | Cover; Title; Copyright; Preface; Contents; Chapter 1: Injectivity and related concepts; 1.A-injective modules; 2. Quasi-injective modules; 3. Exchange and cancellation properties; 4. Decomposition theorems; Comments; Chapter 2: Quasi-continuous modules; 1. Basic properties; 2. Direct sums of quasi-continuous modules; 3. Decompositions of quasi-continuous modules; 4. Internal cancellation property; 5. Quasi-continuity versus quasi-injectivity; Comments; Chapter 3: Continuous modules; 1. Endomorphism rings; 2. Continuous modules; 3. The exchange property; Comments; Chapter 4: Quasi-discrete modules 1. Definition and basic results2. Decomposition theorems; 3. Applications of the decomposition theorems; 4. Discreteness and projectivity; 5. Quasi-discreteness of direct sums; Comments; Chapter 5: Discrete modules; 1. Discrete modules; 2. Endomorphism rings; 3.Commutative noetherian rings; Comments; Appendix; 1. Variants of supplementation; 2. Supplements are summands; 3. Extending modules; 4. The historial origin of the concept of; 5.N -continuity; 6. Open questions; Bibliography; Notation; Index |
| ctrlnum | (OCoLC)839305296 |
| dewey-full | 512/.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.4 |
| dewey-search | 512/.4 |
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| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn839305296 |
| illustrated | Not Illustrated |
| indexdate | 2025-04-11T08:41:21Z |
| institution | BVB |
| isbn | 9781107361669 1107361664 9780511892523 0511892527 |
| language | English |
| oclc_num | 839305296 |
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| publishDate | 1990 |
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| series | London Mathematical Society lecture note series ; |
| series2 | London Mathematical Society lecture note series ; |
| spelling | Mohamed, Saad H. Continuous and discrete modules / Saad H. Mohamed, Bruno J. Müller. Cambridge ; New York : Cambridge University Press, 1990. 1 online resource (126 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series ; 147 Includes bibliographical references (pages 108-121) and index. Print version record. Continuous and discrete modules are, essentially, generalizations of infective and projective modules respectively. Continuous modules provide an appropriate setting for decomposition theory of von Neumann algebras and have important applications to C*-algebras. Discrete modules constitute a dual concept and are related to number theory and algebraic geometry: they possess perfect decomposition properties. The advantage of both types of module is that the Krull-Schmidt theorem can be applied, in part, to them. The authors present here a complete account of the subject and at the same time give a unified picture of the theory. The treatment is essentially self-contained, with background facts being summarized in the first chapter. This book will be useful therefore either to individuals beginning research, or the more experienced worker in algebra and representation theory. Cover; Title; Copyright; Preface; Contents; Chapter 1: Injectivity and related concepts; 1.A-injective modules; 2. Quasi-injective modules; 3. Exchange and cancellation properties; 4. Decomposition theorems; Comments; Chapter 2: Quasi-continuous modules; 1. Basic properties; 2. Direct sums of quasi-continuous modules; 3. Decompositions of quasi-continuous modules; 4. Internal cancellation property; 5. Quasi-continuity versus quasi-injectivity; Comments; Chapter 3: Continuous modules; 1. Endomorphism rings; 2. Continuous modules; 3. The exchange property; Comments; Chapter 4: Quasi-discrete modules 1. Definition and basic results2. Decomposition theorems; 3. Applications of the decomposition theorems; 4. Discreteness and projectivity; 5. Quasi-discreteness of direct sums; Comments; Chapter 5: Discrete modules; 1. Discrete modules; 2. Endomorphism rings; 3.Commutative noetherian rings; Comments; Appendix; 1. Variants of supplementation; 2. Supplements are summands; 3. Extending modules; 4. The historial origin of the concept of; 5.N -continuity; 6. Open questions; Bibliography; Notation; Index Injective modules (Algebra) http://id.loc.gov/authorities/subjects/sh85066449 Projective modules (Algebra) http://id.loc.gov/authorities/subjects/sh85107381 Representations of rings (Algebra) http://id.loc.gov/authorities/subjects/sh85112945 Decomposition (Mathematics) http://id.loc.gov/authorities/subjects/sh85036222 Modules injectifs (Algèbre) Modules projectifs (Algèbre) Représentations d'anneaux (Algèbre) Décomposition (Mathématiques) MATHEMATICS Algebra Intermediate. bisacsh Decomposition (Mathematics) fast Injective modules (Algebra) fast Projective modules (Algebra) fast Representations of rings (Algebra) fast Stetiger Modul gnd http://d-nb.info/gnd/4200110-9 Diskreter Modul gnd http://d-nb.info/gnd/4232089-6 Modules (Algèbre) ram Müller, Bruno J. Print version: Mohamed, Saad H. Continuous and discrete modules. Cambridge ; New York : Cambridge University Press, 1990 0521399750 (DLC) 91168120 (OCoLC)21351057 London Mathematical Society lecture note series ; 147. http://id.loc.gov/authorities/names/n42015587 |
| spellingShingle | Mohamed, Saad H. Continuous and discrete modules / London Mathematical Society lecture note series ; Cover; Title; Copyright; Preface; Contents; Chapter 1: Injectivity and related concepts; 1.A-injective modules; 2. Quasi-injective modules; 3. Exchange and cancellation properties; 4. Decomposition theorems; Comments; Chapter 2: Quasi-continuous modules; 1. Basic properties; 2. Direct sums of quasi-continuous modules; 3. Decompositions of quasi-continuous modules; 4. Internal cancellation property; 5. Quasi-continuity versus quasi-injectivity; Comments; Chapter 3: Continuous modules; 1. Endomorphism rings; 2. Continuous modules; 3. The exchange property; Comments; Chapter 4: Quasi-discrete modules 1. Definition and basic results2. Decomposition theorems; 3. Applications of the decomposition theorems; 4. Discreteness and projectivity; 5. Quasi-discreteness of direct sums; Comments; Chapter 5: Discrete modules; 1. Discrete modules; 2. Endomorphism rings; 3.Commutative noetherian rings; Comments; Appendix; 1. Variants of supplementation; 2. Supplements are summands; 3. Extending modules; 4. The historial origin of the concept of; 5.N -continuity; 6. Open questions; Bibliography; Notation; Index Injective modules (Algebra) http://id.loc.gov/authorities/subjects/sh85066449 Projective modules (Algebra) http://id.loc.gov/authorities/subjects/sh85107381 Representations of rings (Algebra) http://id.loc.gov/authorities/subjects/sh85112945 Decomposition (Mathematics) http://id.loc.gov/authorities/subjects/sh85036222 Modules injectifs (Algèbre) Modules projectifs (Algèbre) Représentations d'anneaux (Algèbre) Décomposition (Mathématiques) MATHEMATICS Algebra Intermediate. bisacsh Decomposition (Mathematics) fast Injective modules (Algebra) fast Projective modules (Algebra) fast Representations of rings (Algebra) fast Stetiger Modul gnd http://d-nb.info/gnd/4200110-9 Diskreter Modul gnd http://d-nb.info/gnd/4232089-6 Modules (Algèbre) ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85066449 http://id.loc.gov/authorities/subjects/sh85107381 http://id.loc.gov/authorities/subjects/sh85112945 http://id.loc.gov/authorities/subjects/sh85036222 http://d-nb.info/gnd/4200110-9 http://d-nb.info/gnd/4232089-6 |
| title | Continuous and discrete modules / |
| title_auth | Continuous and discrete modules / |
| title_exact_search | Continuous and discrete modules / |
| title_full | Continuous and discrete modules / Saad H. Mohamed, Bruno J. Müller. |
| title_fullStr | Continuous and discrete modules / Saad H. Mohamed, Bruno J. Müller. |
| title_full_unstemmed | Continuous and discrete modules / Saad H. Mohamed, Bruno J. Müller. |
| title_short | Continuous and discrete modules / |
| title_sort | continuous and discrete modules |
| topic | Injective modules (Algebra) http://id.loc.gov/authorities/subjects/sh85066449 Projective modules (Algebra) http://id.loc.gov/authorities/subjects/sh85107381 Representations of rings (Algebra) http://id.loc.gov/authorities/subjects/sh85112945 Decomposition (Mathematics) http://id.loc.gov/authorities/subjects/sh85036222 Modules injectifs (Algèbre) Modules projectifs (Algèbre) Représentations d'anneaux (Algèbre) Décomposition (Mathématiques) MATHEMATICS Algebra Intermediate. bisacsh Decomposition (Mathematics) fast Injective modules (Algebra) fast Projective modules (Algebra) fast Representations of rings (Algebra) fast Stetiger Modul gnd http://d-nb.info/gnd/4200110-9 Diskreter Modul gnd http://d-nb.info/gnd/4232089-6 Modules (Algèbre) ram |
| topic_facet | Injective modules (Algebra) Projective modules (Algebra) Representations of rings (Algebra) Decomposition (Mathematics) Modules injectifs (Algèbre) Modules projectifs (Algèbre) Représentations d'anneaux (Algèbre) Décomposition (Mathématiques) MATHEMATICS Algebra Intermediate. Stetiger Modul Diskreter Modul Modules (Algèbre) |
| work_keys_str_mv | AT mohamedsaadh continuousanddiscretemodules AT mullerbrunoj continuousanddiscretemodules |