Modules over endomorphism rings:
This is an extensive synthesis of recent work in the study of endomorphism rings and their modules, bringing together direct sum decompositions of modules, the class number of an algebraic number field, point set topological spaces, and classical noncommutative localization. The main idea behind the...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2010
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications
volume 130 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | This is an extensive synthesis of recent work in the study of endomorphism rings and their modules, bringing together direct sum decompositions of modules, the class number of an algebraic number field, point set topological spaces, and classical noncommutative localization. The main idea behind the book is to study modules G over a ring R via their endomorphism ring EndR(G). The author discusses a wealth of results that classify G and EndR(G) via numerous properties, and in particular results from point set topology are used to provide a complete characterization of the direct sum decomposition properties of G. For graduate students this is a useful introduction, while the more experienced mathematician will discover that the book contains results that are not otherwise available. Each chapter contains a list of exercises and problems for future research, which provide a springboard for students entering modern professional mathematics |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xx, 372 pages) |
| ISBN: | 9781139087346 |
| DOI: | 10.1017/CBO9781139087346 |
Internformat
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| 245 | 1 | 0 | |a Modules over endomorphism rings |c Theodore G. Faticoni |
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| 300 | |a 1 online resource (xx, 372 pages) | ||
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| 490 | 0 | |a Encyclopedia of mathematics and its applications |v volume 130 | |
| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 505 | 8 | |a 1. Preliminary results -- 2. Class number of an abelian group -- 3. Mayer-Victoris sequences -- 4. Lifting units -- 5. conductor -- 6. Conductors and groups -- 7. Invertible fractional ideals -- 8. L-groups -- 9. Modules and homotopy classes -- 10. Tensor functor equivalences -- 11. Characterizing endomorphisms -- 12. Projective modules -- 13. Finitely generated modules -- 14. Rtffr E-projective groups -- 15. Injective endomorphism modules -- 16. diagram of categories -- 17. Diagrams of abelian groups -- 18. Marginal isomorphisms | |
| 520 | |a This is an extensive synthesis of recent work in the study of endomorphism rings and their modules, bringing together direct sum decompositions of modules, the class number of an algebraic number field, point set topological spaces, and classical noncommutative localization. The main idea behind the book is to study modules G over a ring R via their endomorphism ring EndR(G). The author discusses a wealth of results that classify G and EndR(G) via numerous properties, and in particular results from point set topology are used to provide a complete characterization of the direct sum decomposition properties of G. For graduate students this is a useful introduction, while the more experienced mathematician will discover that the book contains results that are not otherwise available. Each chapter contains a list of exercises and problems for future research, which provide a springboard for students entering modern professional mathematics | ||
| 650 | 4 | |a Endomorphism rings | |
| 650 | 4 | |a Modules (Algebra) | |
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Datensatz im Suchindex
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| author | Faticoni, Theodore G. 1954- |
| author_facet | Faticoni, Theodore G. 1954- |
| author_role | aut |
| author_sort | Faticoni, Theodore G. 1954- |
| author_variant | t g f tg tgf |
| building | Verbundindex |
| bvnumber | BV043941706 |
| classification_rvk | SK 230 |
| collection | ZDB-20-CBO |
| contents | 1. Preliminary results -- 2. Class number of an abelian group -- 3. Mayer-Victoris sequences -- 4. Lifting units -- 5. conductor -- 6. Conductors and groups -- 7. Invertible fractional ideals -- 8. L-groups -- 9. Modules and homotopy classes -- 10. Tensor functor equivalences -- 11. Characterizing endomorphisms -- 12. Projective modules -- 13. Finitely generated modules -- 14. Rtffr E-projective groups -- 15. Injective endomorphism modules -- 16. diagram of categories -- 17. Diagrams of abelian groups -- 18. Marginal isomorphisms |
| ctrlnum | (ZDB-20-CBO)CR9781139087346 (OCoLC)862995236 (DE-599)BVBBV043941706 |
| 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 | 3512.4 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9781139087346 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9781139087346 |
| language | English |
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| physical | 1 online resource (xx, 372 pages) |
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| publishDate | 2010 |
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| spelling | Faticoni, Theodore G. 1954- Verfasser aut Modules over endomorphism rings Theodore G. Faticoni Cambridge Cambridge University Press 2010 1 online resource (xx, 372 pages) txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications volume 130 Title from publisher's bibliographic system (viewed on 05 Oct 2015) 1. Preliminary results -- 2. Class number of an abelian group -- 3. Mayer-Victoris sequences -- 4. Lifting units -- 5. conductor -- 6. Conductors and groups -- 7. Invertible fractional ideals -- 8. L-groups -- 9. Modules and homotopy classes -- 10. Tensor functor equivalences -- 11. Characterizing endomorphisms -- 12. Projective modules -- 13. Finitely generated modules -- 14. Rtffr E-projective groups -- 15. Injective endomorphism modules -- 16. diagram of categories -- 17. Diagrams of abelian groups -- 18. Marginal isomorphisms This is an extensive synthesis of recent work in the study of endomorphism rings and their modules, bringing together direct sum decompositions of modules, the class number of an algebraic number field, point set topological spaces, and classical noncommutative localization. The main idea behind the book is to study modules G over a ring R via their endomorphism ring EndR(G). The author discusses a wealth of results that classify G and EndR(G) via numerous properties, and in particular results from point set topology are used to provide a complete characterization of the direct sum decomposition properties of G. For graduate students this is a useful introduction, while the more experienced mathematician will discover that the book contains results that are not otherwise available. Each chapter contains a list of exercises and problems for future research, which provide a springboard for students entering modern professional mathematics Endomorphism rings Modules (Algebra) Modul (DE-588)4129770-2 gnd rswk-swf Endomorphismus (DE-588)4280121-7 gnd rswk-swf Endomorphismus (DE-588)4280121-7 s Modul (DE-588)4129770-2 s 1\p DE-604 Erscheint auch als Druckausgabe 978-0-521-19960-5 https://doi.org/10.1017/CBO9781139087346 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Faticoni, Theodore G. 1954- Modules over endomorphism rings 1. Preliminary results -- 2. Class number of an abelian group -- 3. Mayer-Victoris sequences -- 4. Lifting units -- 5. conductor -- 6. Conductors and groups -- 7. Invertible fractional ideals -- 8. L-groups -- 9. Modules and homotopy classes -- 10. Tensor functor equivalences -- 11. Characterizing endomorphisms -- 12. Projective modules -- 13. Finitely generated modules -- 14. Rtffr E-projective groups -- 15. Injective endomorphism modules -- 16. diagram of categories -- 17. Diagrams of abelian groups -- 18. Marginal isomorphisms Endomorphism rings Modules (Algebra) Modul (DE-588)4129770-2 gnd Endomorphismus (DE-588)4280121-7 gnd |
| subject_GND | (DE-588)4129770-2 (DE-588)4280121-7 |
| title | Modules over endomorphism rings |
| title_auth | Modules over endomorphism rings |
| title_exact_search | Modules over endomorphism rings |
| title_full | Modules over endomorphism rings Theodore G. Faticoni |
| title_fullStr | Modules over endomorphism rings Theodore G. Faticoni |
| title_full_unstemmed | Modules over endomorphism rings Theodore G. Faticoni |
| title_short | Modules over endomorphism rings |
| title_sort | modules over endomorphism rings |
| topic | Endomorphism rings Modules (Algebra) Modul (DE-588)4129770-2 gnd Endomorphismus (DE-588)4280121-7 gnd |
| topic_facet | Endomorphism rings Modules (Algebra) Modul Endomorphismus |
| url | https://doi.org/10.1017/CBO9781139087346 |
| work_keys_str_mv | AT faticonitheodoreg modulesoverendomorphismrings |