Homological algebra:
When this book was written, methods of algebraic topology had caused revolutions in the world of pure algebra. To clarify the advances that had been made, Cartan and Eilenberg tried to unify the fields and to construct the framework of a fully fledged theory. The invasion of algebra had occurred on...
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| Hauptverfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, NJ
Princeton University Press
[2016]
|
| Schriftenreihe: | Princeton mathematical series
19 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | When this book was written, methods of algebraic topology had caused revolutions in the world of pure algebra. To clarify the advances that had been made, Cartan and Eilenberg tried to unify the fields and to construct the framework of a fully fledged theory. The invasion of algebra had occurred on three fronts through the construction of cohomology theories for groups, Lie algebras, and associative algebras. This book presents a single homology (and also cohomology) theory that embodies all three; a large number of results is thus established in a general framework. Subsequently, each of the three theories is singled out by a suitable specialization, and its specific properties are studied. The starting point is the notion of a module over a ring. The primary operations are the tensor product of two modules and the groups of all homomorphisms of one module into another. From these, "higher order" derived of operations are obtained, which enjoy all the properties usually attributed to homology theories. This leads in a natural way to the study of "functors" and of their "derived functors." This mathematical masterpiece will appeal to all mathematicians working in algebraic topology |
| Beschreibung: | Description based on online resource; title from PDF title page (publisher's Web site, viewed Sep. 08, 2016) |
| Beschreibung: | 1 Online-Ressource |
| ISBN: | 9781400883844 |
| DOI: | 10.1515/9781400883844 |
Internformat
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| 500 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed Sep. 08, 2016) | ||
| 520 | |a When this book was written, methods of algebraic topology had caused revolutions in the world of pure algebra. To clarify the advances that had been made, Cartan and Eilenberg tried to unify the fields and to construct the framework of a fully fledged theory. The invasion of algebra had occurred on three fronts through the construction of cohomology theories for groups, Lie algebras, and associative algebras. This book presents a single homology (and also cohomology) theory that embodies all three; a large number of results is thus established in a general framework. Subsequently, each of the three theories is singled out by a suitable specialization, and its specific properties are studied. The starting point is the notion of a module over a ring. The primary operations are the tensor product of two modules and the groups of all homomorphisms of one module into another. From these, "higher order" derived of operations are obtained, which enjoy all the properties usually attributed to homology theories. This leads in a natural way to the study of "functors" and of their "derived functors." This mathematical masterpiece will appeal to all mathematicians working in algebraic topology | ||
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Datensatz im Suchindex
| _version_ | 1804176753281728512 |
|---|---|
| any_adam_object | |
| author | Cartan, Henri 1904-2008 Eilenberg, Samuel 1913-1998 |
| author_GND | (DE-588)118668625 (DE-588)119020769 |
| author_facet | Cartan, Henri 1904-2008 Eilenberg, Samuel 1913-1998 |
| author_role | aut aut |
| author_sort | Cartan, Henri 1904-2008 |
| author_variant | h c hc s e se |
| building | Verbundindex |
| bvnumber | BV043867685 |
| collection | ZDB-23-DGG ZDB-23-PMS |
| ctrlnum | (ZDB-23-DGG)9781400883844 (OCoLC)948780067 (DE-599)BVBBV043867685 |
| dewey-full | 513.83 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 513 - Arithmetic |
| dewey-raw | 513.83 |
| dewey-search | 513.83 |
| dewey-sort | 3513.83 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1515/9781400883844 |
| format | Electronic eBook |
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| id | DE-604.BV043867685 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:37:11Z |
| institution | BVB |
| isbn | 9781400883844 |
| language | English |
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| publishDate | 2016 |
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| publisher | Princeton University Press |
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| series | Princeton mathematical series |
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| spelling | Cartan, Henri 1904-2008 (DE-588)118668625 aut Homological algebra Samuel Eilenberg, Henry Cartan Princeton, NJ Princeton University Press [2016] © 1956 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Princeton mathematical series 19 Description based on online resource; title from PDF title page (publisher's Web site, viewed Sep. 08, 2016) When this book was written, methods of algebraic topology had caused revolutions in the world of pure algebra. To clarify the advances that had been made, Cartan and Eilenberg tried to unify the fields and to construct the framework of a fully fledged theory. The invasion of algebra had occurred on three fronts through the construction of cohomology theories for groups, Lie algebras, and associative algebras. This book presents a single homology (and also cohomology) theory that embodies all three; a large number of results is thus established in a general framework. Subsequently, each of the three theories is singled out by a suitable specialization, and its specific properties are studied. The starting point is the notion of a module over a ring. The primary operations are the tensor product of two modules and the groups of all homomorphisms of one module into another. From these, "higher order" derived of operations are obtained, which enjoy all the properties usually attributed to homology theories. This leads in a natural way to the study of "functors" and of their "derived functors." This mathematical masterpiece will appeal to all mathematicians working in algebraic topology Algebra, Homological Homologische Algebra (DE-588)4160598-6 gnd rswk-swf Homologische Algebra (DE-588)4160598-6 s 1\p DE-604 Eilenberg, Samuel 1913-1998 (DE-588)119020769 aut Princeton mathematical series 19 (DE-604)BV045898993 19 https://doi.org/10.1515/9781400883844?locatt=mode:legacy Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Cartan, Henri 1904-2008 Eilenberg, Samuel 1913-1998 Homological algebra Princeton mathematical series Algebra, Homological Homologische Algebra (DE-588)4160598-6 gnd |
| subject_GND | (DE-588)4160598-6 |
| title | Homological algebra |
| title_auth | Homological algebra |
| title_exact_search | Homological algebra |
| title_full | Homological algebra Samuel Eilenberg, Henry Cartan |
| title_fullStr | Homological algebra Samuel Eilenberg, Henry Cartan |
| title_full_unstemmed | Homological algebra Samuel Eilenberg, Henry Cartan |
| title_short | Homological algebra |
| title_sort | homological algebra |
| topic | Algebra, Homological Homologische Algebra (DE-588)4160598-6 gnd |
| topic_facet | Algebra, Homological Homologische Algebra |
| url | https://doi.org/10.1515/9781400883844?locatt=mode:legacy |
| volume_link | (DE-604)BV045898993 |
| work_keys_str_mv | AT cartanhenri homologicalalgebra AT eilenbergsamuel homologicalalgebra |