Galois theories:
Starting from the classical finite-dimensional Galois theory of fields, this book develops Galois theory in a much more general context, presenting work by Grothendieck in terms of separable algebras and then proceeding to the infinite-dimensional case, which requires considering topological Galois...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2001
|
| Schriftenreihe: | Cambridge studies in advanced mathematics
72 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBR01 Volltext |
| Zusammenfassung: | Starting from the classical finite-dimensional Galois theory of fields, this book develops Galois theory in a much more general context, presenting work by Grothendieck in terms of separable algebras and then proceeding to the infinite-dimensional case, which requires considering topological Galois groups. In the core of the book, the authors first formalize the categorical context in which a general Galois theorem holds, and then give applications to Galois theory for commutative rings, central extensions of groups, the topological theory of covering maps and a Galois theorem for toposes. The book is designed to be accessible to a wide audience: the prerequisites are first courses in algebra and general topology, together with some familiarity with the categorical notions of limit and adjoint functors. The first chapters are accessible to advanced undergraduates, with later ones at a graduate level. For all algebraists and category theorists this book will be a rewarding read |
| Beschreibung: | 1 online resource (xiv, 341 Seiten) |
| ISBN: | 9780511619939 |
| DOI: | 10.1017/CBO9780511619939 |
Internformat
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| 100 | 1 | |a Borceux, Francis |d 1948- |e Verfasser |0 (DE-588)11084825X |4 aut | |
| 245 | 1 | 0 | |a Galois theories |c Francis Borceux, George Janelidze |
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| 490 | 1 | |a Cambridge studies in advanced mathematics |v 72 | |
| 505 | 8 | 0 | |t Classical galois theory |t Galois theory of grothendieck |t Infinitary galois theory |t Categorical galois theory of commuttive rings |t Categorical galois theorem and factorization systems |t Covering maps |t Non-galoisian galois theory |
| 520 | |a Starting from the classical finite-dimensional Galois theory of fields, this book develops Galois theory in a much more general context, presenting work by Grothendieck in terms of separable algebras and then proceeding to the infinite-dimensional case, which requires considering topological Galois groups. In the core of the book, the authors first formalize the categorical context in which a general Galois theorem holds, and then give applications to Galois theory for commutative rings, central extensions of groups, the topological theory of covering maps and a Galois theorem for toposes. The book is designed to be accessible to a wide audience: the prerequisites are first courses in algebra and general topology, together with some familiarity with the categorical notions of limit and adjoint functors. The first chapters are accessible to advanced undergraduates, with later ones at a graduate level. For all algebraists and category theorists this book will be a rewarding read | ||
| 650 | 4 | |a Galois theory | |
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| 689 | 0 | 0 | |a Galois-Theorie |0 (DE-588)4155901-0 |D s |
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| 700 | 1 | |a Janelidze, George |d 1952- |e Sonstige |0 (DE-588)142255319 |4 oth | |
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Datensatz im Suchindex
| _version_ | 1804176884037058560 |
|---|---|
| any_adam_object | |
| author | Borceux, Francis 1948- |
| author_GND | (DE-588)11084825X (DE-588)142255319 |
| author_facet | Borceux, Francis 1948- |
| author_role | aut |
| author_sort | Borceux, Francis 1948- |
| author_variant | f b fb |
| building | Verbundindex |
| bvnumber | BV043941833 |
| classification_rvk | SK 230 SK 200 |
| collection | ZDB-20-CBO |
| contents | Classical galois theory Galois theory of grothendieck Infinitary galois theory Categorical galois theory of commuttive rings Categorical galois theorem and factorization systems Covering maps Non-galoisian galois theory |
| ctrlnum | (ZDB-20-CBO)CR9780511619939 (OCoLC)992925703 (DE-599)BVBBV043941833 |
| dewey-full | 512/.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.3 |
| dewey-search | 512/.3 |
| dewey-sort | 3512 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511619939 |
| format | Electronic eBook |
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| id | DE-604.BV043941833 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511619939 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350803 |
| oclc_num | 992925703 |
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| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR DE-83 |
| physical | 1 online resource (xiv, 341 Seiten) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO ZDB-20-CBO UBR Einzelkauf (Lückenergänzung CUP Serien 2018) |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Cambridge University Press |
| record_format | marc |
| series | Cambridge studies in advanced mathematics |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Borceux, Francis 1948- Verfasser (DE-588)11084825X aut Galois theories Francis Borceux, George Janelidze Cambridge Cambridge University Press 2001 1 online resource (xiv, 341 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge studies in advanced mathematics 72 Classical galois theory Galois theory of grothendieck Infinitary galois theory Categorical galois theory of commuttive rings Categorical galois theorem and factorization systems Covering maps Non-galoisian galois theory Starting from the classical finite-dimensional Galois theory of fields, this book develops Galois theory in a much more general context, presenting work by Grothendieck in terms of separable algebras and then proceeding to the infinite-dimensional case, which requires considering topological Galois groups. In the core of the book, the authors first formalize the categorical context in which a general Galois theorem holds, and then give applications to Galois theory for commutative rings, central extensions of groups, the topological theory of covering maps and a Galois theorem for toposes. The book is designed to be accessible to a wide audience: the prerequisites are first courses in algebra and general topology, together with some familiarity with the categorical notions of limit and adjoint functors. The first chapters are accessible to advanced undergraduates, with later ones at a graduate level. For all algebraists and category theorists this book will be a rewarding read Galois theory Galois-Theorie (DE-588)4155901-0 gnd rswk-swf Galois-Theorie (DE-588)4155901-0 s DE-604 Janelidze, George 1952- Sonstige (DE-588)142255319 oth Erscheint auch als Druck-Ausgabe 978-0-521-80309-0 Erscheint auch als Druck-Ausgabe 978-0-521-07041-6 Cambridge studies in advanced mathematics 72 (DE-604)BV044781283 72 https://doi.org/10.1017/CBO9780511619939 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Borceux, Francis 1948- Galois theories Cambridge studies in advanced mathematics Classical galois theory Galois theory of grothendieck Infinitary galois theory Categorical galois theory of commuttive rings Categorical galois theorem and factorization systems Covering maps Non-galoisian galois theory Galois theory Galois-Theorie (DE-588)4155901-0 gnd |
| subject_GND | (DE-588)4155901-0 |
| title | Galois theories |
| title_alt | Classical galois theory Galois theory of grothendieck Infinitary galois theory Categorical galois theory of commuttive rings Categorical galois theorem and factorization systems Covering maps Non-galoisian galois theory |
| title_auth | Galois theories |
| title_exact_search | Galois theories |
| title_full | Galois theories Francis Borceux, George Janelidze |
| title_fullStr | Galois theories Francis Borceux, George Janelidze |
| title_full_unstemmed | Galois theories Francis Borceux, George Janelidze |
| title_short | Galois theories |
| title_sort | galois theories |
| topic | Galois theory Galois-Theorie (DE-588)4155901-0 gnd |
| topic_facet | Galois theory Galois-Theorie |
| url | https://doi.org/10.1017/CBO9780511619939 |
| volume_link | (DE-604)BV044781283 |
| work_keys_str_mv | AT borceuxfrancis galoistheories AT janelidzegeorge galoistheories |