Rings and Categories of Modules:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer
1992
|
| Ausgabe: | Second Edition |
| Schriftenreihe: | Graduate Texts in Mathematics
13 |
| Schlagworte: | |
| Online-Zugang: | UPA01 Volltext |
| Beschreibung: | This book is intended to provide a reasonably self-contained account of a major portion of the general theory of rings and modules suitable as a text for introductory and more advanced graduate courses. We assume the famil iarity with rings usually acquired in standard undergraduate algebra courses. Our general approach is categorical rather than arithmetical. The continuing theme of the text is the study of the relationship between the one-sided ideal structure that a ring may possess and the behavior of its categories of modules. Following a brief outline of set-theoretic and categorical foundations, the text begins with the basic definitions and properties of rings, modules and homomorphisms and ranges through comprehensive treatments of direct sums, finiteness conditions, the Wedderburn-Artin Theorem, the Jacobson radical, the hom and tensor functions, Morita equivalence and duality, de composition theory of injective and projective modules, and semi perfect and perfect rings. In this second edition we have included a chapter containing many of the classical results on artinian rings that have hdped to form the foundation for much of the contemporary research on the representation theory of artinian rings and finite dimensional algebras. Both to illustrate the text and to extend it we have included a substantial number of exercises covering a wide spectrum of difficulty. There are, of course" many important areas of ring and module theory that the text does not touch upon |
| Beschreibung: | 1 Online-Ressource (VIII, 376 Seiten) |
| ISBN: | 9781461244189 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4612-4418-9 |
Internformat
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| 490 | 1 | |a Graduate Texts in Mathematics |v 13 |x 0072-5285 | |
| 500 | |a This book is intended to provide a reasonably self-contained account of a major portion of the general theory of rings and modules suitable as a text for introductory and more advanced graduate courses. We assume the famil iarity with rings usually acquired in standard undergraduate algebra courses. Our general approach is categorical rather than arithmetical. The continuing theme of the text is the study of the relationship between the one-sided ideal structure that a ring may possess and the behavior of its categories of modules. Following a brief outline of set-theoretic and categorical foundations, the text begins with the basic definitions and properties of rings, modules and homomorphisms and ranges through comprehensive treatments of direct sums, finiteness conditions, the Wedderburn-Artin Theorem, the Jacobson radical, the hom and tensor functions, Morita equivalence and duality, de composition theory of injective and projective modules, and semi perfect and perfect rings. In this second edition we have included a chapter containing many of the classical results on artinian rings that have hdped to form the foundation for much of the contemporary research on the representation theory of artinian rings and finite dimensional algebras. Both to illustrate the text and to extend it we have included a substantial number of exercises covering a wide spectrum of difficulty. There are, of course" many important areas of ring and module theory that the text does not touch upon | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Anderson, Frank W. 1928-2016 |
| author_GND | (DE-588)108107671 (DE-588)10810768X |
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| author_role | aut |
| author_sort | Anderson, Frank W. 1928-2016 |
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| dewey-ones | 512 - Algebra |
| dewey-raw | 512 |
| dewey-search | 512 |
| dewey-sort | 3512 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-4418-9 |
| edition | Second Edition |
| format | Electronic eBook |
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| id | DE-604.BV042420286 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:06Z |
| institution | BVB |
| isbn | 9781461244189 |
| issn | 0072-5285 |
| language | English |
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| physical | 1 Online-Ressource (VIII, 376 Seiten) |
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| publishDate | 1992 |
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| publisher | Springer |
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| series | Graduate Texts in Mathematics |
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| spelling | Anderson, Frank W. 1928-2016 Verfasser (DE-588)108107671 aut Rings and Categories of Modules by Frank W. Anderson, Kent R. Fuller Second Edition New York, NY Springer 1992 1 Online-Ressource (VIII, 376 Seiten) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 13 0072-5285 This book is intended to provide a reasonably self-contained account of a major portion of the general theory of rings and modules suitable as a text for introductory and more advanced graduate courses. We assume the famil iarity with rings usually acquired in standard undergraduate algebra courses. Our general approach is categorical rather than arithmetical. The continuing theme of the text is the study of the relationship between the one-sided ideal structure that a ring may possess and the behavior of its categories of modules. Following a brief outline of set-theoretic and categorical foundations, the text begins with the basic definitions and properties of rings, modules and homomorphisms and ranges through comprehensive treatments of direct sums, finiteness conditions, the Wedderburn-Artin Theorem, the Jacobson radical, the hom and tensor functions, Morita equivalence and duality, de composition theory of injective and projective modules, and semi perfect and perfect rings. In this second edition we have included a chapter containing many of the classical results on artinian rings that have hdped to form the foundation for much of the contemporary research on the representation theory of artinian rings and finite dimensional algebras. Both to illustrate the text and to extend it we have included a substantial number of exercises covering a wide spectrum of difficulty. There are, of course" many important areas of ring and module theory that the text does not touch upon Mathematics Algebra Mathematik Modul (DE-588)4129770-2 gnd rswk-swf Ring Mathematik (DE-588)4128084-2 gnd rswk-swf Kategorie Mathematik (DE-588)4129930-9 gnd rswk-swf Ring Mathematik (DE-588)4128084-2 s Modul (DE-588)4129770-2 s Kategorie Mathematik (DE-588)4129930-9 s 1\p DE-604 Fuller, Kent R. 1938- Sonstige (DE-588)10810768X oth Erscheint auch als Druck-Ausgabe, Hardcover 978-0-387-97845-1 Erscheint auch als Druck-Ausgabe, Paperback 978-1-46128763-6 Graduate Texts in Mathematics 13 (DE-604)BV035421258 13 https://doi.org/10.1007/978-1-4612-4418-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Anderson, Frank W. 1928-2016 Rings and Categories of Modules Graduate Texts in Mathematics Mathematics Algebra Mathematik Modul (DE-588)4129770-2 gnd Ring Mathematik (DE-588)4128084-2 gnd Kategorie Mathematik (DE-588)4129930-9 gnd |
| subject_GND | (DE-588)4129770-2 (DE-588)4128084-2 (DE-588)4129930-9 |
| title | Rings and Categories of Modules |
| title_auth | Rings and Categories of Modules |
| title_exact_search | Rings and Categories of Modules |
| title_full | Rings and Categories of Modules by Frank W. Anderson, Kent R. Fuller |
| title_fullStr | Rings and Categories of Modules by Frank W. Anderson, Kent R. Fuller |
| title_full_unstemmed | Rings and Categories of Modules by Frank W. Anderson, Kent R. Fuller |
| title_short | Rings and Categories of Modules |
| title_sort | rings and categories of modules |
| topic | Mathematics Algebra Mathematik Modul (DE-588)4129770-2 gnd Ring Mathematik (DE-588)4128084-2 gnd Kategorie Mathematik (DE-588)4129930-9 gnd |
| topic_facet | Mathematics Algebra Mathematik Modul Ring Mathematik Kategorie Mathematik |
| url | https://doi.org/10.1007/978-1-4612-4418-9 |
| volume_link | (DE-604)BV035421258 |
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