Corings and comodules:
Corings and comodules are fundamental algebraic structures, which can be thought of as both dualisations and generalisations of rings and modules. Introduced by Sweedler in 1975, only recently they have been shown to have far reaching applications ranging from the category theory including different...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2003
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| Schriftenreihe: | London Mathematical Society lecture note series
309 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | Corings and comodules are fundamental algebraic structures, which can be thought of as both dualisations and generalisations of rings and modules. Introduced by Sweedler in 1975, only recently they have been shown to have far reaching applications ranging from the category theory including differential graded categories through classical and Hopf-type module theory to non-commutative geometry and mathematical physics. This is the first extensive treatment of the theory of corings and their comodules. In the first part, the module-theoretic aspects of coalgebras over commutative rings are described. Corings are then defined as coalgebras over non-commutative rings. Topics covered include module-theoretic aspects of corings, such as the relation of comodules to special subcategories of the category of modules (sigma-type categories), connections between corings and extensions of rings, properties of new examples of corings associated to entwining structures, generalisations of bialgebras such as bialgebroids and weak bialgebras, and the appearance of corings in non-commutative geometry |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (x, 476 pages) |
| ISBN: | 9780511546495 |
| DOI: | 10.1017/CBO9780511546495 |
Internformat
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| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 505 | 8 | |a 1. Coalgebras and comodules -- 2. Bialgebras and Hopf algebras -- 3. Corings and comodules -- 4. Corings and extensions of rings -- 5. Corings and entwining structures -- 6. Weak corings and entwinings | |
| 520 | |a Corings and comodules are fundamental algebraic structures, which can be thought of as both dualisations and generalisations of rings and modules. Introduced by Sweedler in 1975, only recently they have been shown to have far reaching applications ranging from the category theory including differential graded categories through classical and Hopf-type module theory to non-commutative geometry and mathematical physics. This is the first extensive treatment of the theory of corings and their comodules. In the first part, the module-theoretic aspects of coalgebras over commutative rings are described. Corings are then defined as coalgebras over non-commutative rings. Topics covered include module-theoretic aspects of corings, such as the relation of comodules to special subcategories of the category of modules (sigma-type categories), connections between corings and extensions of rings, properties of new examples of corings associated to entwining structures, generalisations of bialgebras such as bialgebroids and weak bialgebras, and the appearance of corings in non-commutative geometry | ||
| 650 | 4 | |a Corings (Algebra) | |
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| 700 | 1 | |a Wisbauer, Robert |d 1941- |e Sonstige |0 (DE-588)108295044 |4 oth | |
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Datensatz im Suchindex
| _version_ | 1804176883684737024 |
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| any_adam_object | |
| author | Brzeziński, Tomasz 1966- |
| author_GND | (DE-588)13561175X (DE-588)108295044 |
| author_facet | Brzeziński, Tomasz 1966- |
| author_role | aut |
| author_sort | Brzeziński, Tomasz 1966- |
| author_variant | t b tb |
| building | Verbundindex |
| bvnumber | BV043941651 |
| classification_rvk | SI 320 |
| collection | ZDB-20-CBO |
| contents | 1. Coalgebras and comodules -- 2. Bialgebras and Hopf algebras -- 3. Corings and comodules -- 4. Corings and extensions of rings -- 5. Corings and entwining structures -- 6. Weak corings and entwinings |
| ctrlnum | (ZDB-20-CBO)CR9780511546495 (OCoLC)850496330 (DE-599)BVBBV043941651 |
| 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 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511546495 |
| format | Electronic eBook |
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| id | DE-604.BV043941651 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511546495 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350621 |
| oclc_num | 850496330 |
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| owner | DE-12 DE-92 |
| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (x, 476 pages) |
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| publishDate | 2003 |
| publishDateSearch | 2003 |
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| publisher | Cambridge University Press |
| record_format | marc |
| series2 | London Mathematical Society lecture note series |
| spelling | Brzeziński, Tomasz 1966- Verfasser (DE-588)13561175X aut Corings and comodules Tomasz Brzezinski, Robert Wisbauer Corings & Comodules Cambridge Cambridge University Press 2003 1 online resource (x, 476 pages) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 309 Title from publisher's bibliographic system (viewed on 05 Oct 2015) 1. Coalgebras and comodules -- 2. Bialgebras and Hopf algebras -- 3. Corings and comodules -- 4. Corings and extensions of rings -- 5. Corings and entwining structures -- 6. Weak corings and entwinings Corings and comodules are fundamental algebraic structures, which can be thought of as both dualisations and generalisations of rings and modules. Introduced by Sweedler in 1975, only recently they have been shown to have far reaching applications ranging from the category theory including differential graded categories through classical and Hopf-type module theory to non-commutative geometry and mathematical physics. This is the first extensive treatment of the theory of corings and their comodules. In the first part, the module-theoretic aspects of coalgebras over commutative rings are described. Corings are then defined as coalgebras over non-commutative rings. Topics covered include module-theoretic aspects of corings, such as the relation of comodules to special subcategories of the category of modules (sigma-type categories), connections between corings and extensions of rings, properties of new examples of corings associated to entwining structures, generalisations of bialgebras such as bialgebroids and weak bialgebras, and the appearance of corings in non-commutative geometry Corings (Algebra) Comodules Koalgebra (DE-588)4164324-0 gnd rswk-swf Ring Mathematik (DE-588)4128084-2 gnd rswk-swf Modul (DE-588)4129770-2 gnd rswk-swf Koalgebra (DE-588)4164324-0 s Ring Mathematik (DE-588)4128084-2 s Modul (DE-588)4129770-2 s 1\p DE-604 Wisbauer, Robert 1941- Sonstige (DE-588)108295044 oth Erscheint auch als Druckausgabe 978-0-521-53931-9 https://doi.org/10.1017/CBO9780511546495 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Brzeziński, Tomasz 1966- Corings and comodules 1. Coalgebras and comodules -- 2. Bialgebras and Hopf algebras -- 3. Corings and comodules -- 4. Corings and extensions of rings -- 5. Corings and entwining structures -- 6. Weak corings and entwinings Corings (Algebra) Comodules Koalgebra (DE-588)4164324-0 gnd Ring Mathematik (DE-588)4128084-2 gnd Modul (DE-588)4129770-2 gnd |
| subject_GND | (DE-588)4164324-0 (DE-588)4128084-2 (DE-588)4129770-2 |
| title | Corings and comodules |
| title_alt | Corings & Comodules |
| title_auth | Corings and comodules |
| title_exact_search | Corings and comodules |
| title_full | Corings and comodules Tomasz Brzezinski, Robert Wisbauer |
| title_fullStr | Corings and comodules Tomasz Brzezinski, Robert Wisbauer |
| title_full_unstemmed | Corings and comodules Tomasz Brzezinski, Robert Wisbauer |
| title_short | Corings and comodules |
| title_sort | corings and comodules |
| topic | Corings (Algebra) Comodules Koalgebra (DE-588)4164324-0 gnd Ring Mathematik (DE-588)4128084-2 gnd Modul (DE-588)4129770-2 gnd |
| topic_facet | Corings (Algebra) Comodules Koalgebra Ring Mathematik Modul |
| url | https://doi.org/10.1017/CBO9780511546495 |
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