Purity, spectra and localisation:
It is possible to associate a topological space to the category of modules over any ring. This space, the Ziegler spectrum, is based on the indecomposable pure-injective modules. Although the Ziegler spectrum arose within the model theory of modules and plays a central role in that subject, this boo...
Gespeichert in:
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2009
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| Schriftenreihe: | Encyclopedia of mathematics and its applications
volume 121 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 URL des Erstveröffentlichers |
| Zusammenfassung: | It is possible to associate a topological space to the category of modules over any ring. This space, the Ziegler spectrum, is based on the indecomposable pure-injective modules. Although the Ziegler spectrum arose within the model theory of modules and plays a central role in that subject, this book concentrates specifically on its algebraic aspects and uses. The central aim is to understand modules and the categories they form through associated structures and dimensions, which reflect the complexity of these, and similar, categories. The structures and dimensions considered arise particularly through the application of model-theoretic and functor-category ideas and methods. Purity and associated notions are central, localisation is an ever-present theme and various types of spectrum play organising roles. This book presents a unified, coherent account of material which is often presented from very different viewpoints and clarifies the relationships between these various approaches |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 Online-Ressource (xxviii, 769 Seiten) |
| ISBN: | 9781139644242 |
| DOI: | 10.1017/CBO9781139644242 |
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| 505 | 8 | |a Pp conditions -- Purity -- Pp-pairs and definable subcategories -- Pp-types and pure-injectivity -- The Ziegler spectrum -- Rings of definable scalars -- M-dimension and width -- Examples -- Ideals in mod-R -- Finitely presented functors -- Serre subcategories and localisation -- The Ziegler spectrum and injective functors -- Dimensions -- The Zariski spectrum and the sheaf of definable scalars -- Artin algebras -- Finitely accessible and presentable additive categories -- Spectra of triangulated categories -- Definable categories and interpretation functors | |
| 520 | |a It is possible to associate a topological space to the category of modules over any ring. This space, the Ziegler spectrum, is based on the indecomposable pure-injective modules. Although the Ziegler spectrum arose within the model theory of modules and plays a central role in that subject, this book concentrates specifically on its algebraic aspects and uses. The central aim is to understand modules and the categories they form through associated structures and dimensions, which reflect the complexity of these, and similar, categories. The structures and dimensions considered arise particularly through the application of model-theoretic and functor-category ideas and methods. Purity and associated notions are central, localisation is an ever-present theme and various types of spectrum play organising roles. This book presents a unified, coherent account of material which is often presented from very different viewpoints and clarifies the relationships between these various approaches | ||
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Datensatz im Suchindex
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|---|---|
| any_adam_object | |
| author | Prest, Mike 1952- |
| author_GND | (DE-588)141199849 |
| author_facet | Prest, Mike 1952- |
| author_role | aut |
| author_sort | Prest, Mike 1952- |
| author_variant | m p mp |
| building | Verbundindex |
| bvnumber | BV043942101 |
| classification_rvk | SK 230 |
| collection | ZDB-20-CBO |
| contents | Pp conditions -- Purity -- Pp-pairs and definable subcategories -- Pp-types and pure-injectivity -- The Ziegler spectrum -- Rings of definable scalars -- M-dimension and width -- Examples -- Ideals in mod-R -- Finitely presented functors -- Serre subcategories and localisation -- The Ziegler spectrum and injective functors -- Dimensions -- The Zariski spectrum and the sheaf of definable scalars -- Artin algebras -- Finitely accessible and presentable additive categories -- Spectra of triangulated categories -- Definable categories and interpretation functors |
| ctrlnum | (ZDB-20-CBO)CR9781139644242 (OCoLC)890446403 (DE-599)BVBBV043942101 |
| dewey-full | 511.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 |
| dewey-search | 511.3 |
| dewey-sort | 3511.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9781139644242 |
| format | Electronic eBook |
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| id | DE-604.BV043942101 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:17Z |
| institution | BVB |
| isbn | 9781139644242 |
| language | English |
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| physical | 1 Online-Ressource (xxviii, 769 Seiten) |
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| publisher | Cambridge University Press |
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| spelling | Prest, Mike 1952- Verfasser (DE-588)141199849 aut Purity, spectra and localisation Mike Prest Purity, Spectra & Localisation Cambridge Cambridge University Press 2009 1 Online-Ressource (xxviii, 769 Seiten) txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications volume 121 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Pp conditions -- Purity -- Pp-pairs and definable subcategories -- Pp-types and pure-injectivity -- The Ziegler spectrum -- Rings of definable scalars -- M-dimension and width -- Examples -- Ideals in mod-R -- Finitely presented functors -- Serre subcategories and localisation -- The Ziegler spectrum and injective functors -- Dimensions -- The Zariski spectrum and the sheaf of definable scalars -- Artin algebras -- Finitely accessible and presentable additive categories -- Spectra of triangulated categories -- Definable categories and interpretation functors It is possible to associate a topological space to the category of modules over any ring. This space, the Ziegler spectrum, is based on the indecomposable pure-injective modules. Although the Ziegler spectrum arose within the model theory of modules and plays a central role in that subject, this book concentrates specifically on its algebraic aspects and uses. The central aim is to understand modules and the categories they form through associated structures and dimensions, which reflect the complexity of these, and similar, categories. The structures and dimensions considered arise particularly through the application of model-theoretic and functor-category ideas and methods. Purity and associated notions are central, localisation is an ever-present theme and various types of spectrum play organising roles. This book presents a unified, coherent account of material which is often presented from very different viewpoints and clarifies the relationships between these various approaches Logic, Symbolic and mathematical Categories (Mathematics) Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Kategorientheorie (DE-588)4120552-2 gnd rswk-swf Algebra (DE-588)4001156-2 gnd rswk-swf Algebra (DE-588)4001156-2 s Mathematische Logik (DE-588)4037951-6 s Kategorientheorie (DE-588)4120552-2 s 1\p DE-604 Erscheint auch als Druckausgabe 978-0-521-87308-6 Encyclopedia of mathematics and its applications volume 121 (DE-604)BV000903719 121 https://doi.org/10.1017/CBO9781139644242 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Prest, Mike 1952- Purity, spectra and localisation Encyclopedia of mathematics and its applications Pp conditions -- Purity -- Pp-pairs and definable subcategories -- Pp-types and pure-injectivity -- The Ziegler spectrum -- Rings of definable scalars -- M-dimension and width -- Examples -- Ideals in mod-R -- Finitely presented functors -- Serre subcategories and localisation -- The Ziegler spectrum and injective functors -- Dimensions -- The Zariski spectrum and the sheaf of definable scalars -- Artin algebras -- Finitely accessible and presentable additive categories -- Spectra of triangulated categories -- Definable categories and interpretation functors Logic, Symbolic and mathematical Categories (Mathematics) Mathematische Logik (DE-588)4037951-6 gnd Kategorientheorie (DE-588)4120552-2 gnd Algebra (DE-588)4001156-2 gnd |
| subject_GND | (DE-588)4037951-6 (DE-588)4120552-2 (DE-588)4001156-2 |
| title | Purity, spectra and localisation |
| title_alt | Purity, Spectra & Localisation |
| title_auth | Purity, spectra and localisation |
| title_exact_search | Purity, spectra and localisation |
| title_full | Purity, spectra and localisation Mike Prest |
| title_fullStr | Purity, spectra and localisation Mike Prest |
| title_full_unstemmed | Purity, spectra and localisation Mike Prest |
| title_short | Purity, spectra and localisation |
| title_sort | purity spectra and localisation |
| topic | Logic, Symbolic and mathematical Categories (Mathematics) Mathematische Logik (DE-588)4037951-6 gnd Kategorientheorie (DE-588)4120552-2 gnd Algebra (DE-588)4001156-2 gnd |
| topic_facet | Logic, Symbolic and mathematical Categories (Mathematics) Mathematische Logik Kategorientheorie Algebra |
| url | https://doi.org/10.1017/CBO9781139644242 |
| volume_link | (DE-604)BV000903719 |
| work_keys_str_mv | AT prestmike purityspectraandlocalisation AT prestmike purityspectralocalisation |