Symmetric Bilinear Forms:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1973
|
| Schriftenreihe: | Ergebnisse der Mathematik und ihrer Grenzgebiete
73 |
| Schlagwörter: | |
| Links: | https://doi.org/10.1007/978-3-642-88330-9 |
| Beschreibung: | The theory of quadratic forms and the intimately related theory of symmetric bilinear forms have a lang and rich his tory, highlighted by the work of Legendre, Gauss, Minkowski, and Hasse. (Compare [Dickson] and [Bourbaki, 24, p. 185].) Our exposition will concentrate on the relatively recent developments which begin with and are inspired by Witt's 1937 paper "Theorie der quadratischen Formen in beliebigen Körpern." We will be particularly interested in the work of A. Pfister and M. Knebusch. However, some older material will be described, particularly in Chapter II. The presentation is based on lectures by Milnor at the Institute for Advanced Study, and at Haverford College under the Phillips Lecture Program, during the Fall of 1970, as well as lectures at Princeton University in 1966. We want to thank J. Cunningham, M. Knebusch, M. Kneser, A. Rosenberg, W. Scharlau and J.-P. Serre for helpful suggestions and corrections. Prerequisites. The reader should be familiar with the rudiments of algebra, including for example the concept of tensor product for modules over a commutative ring. A few individual sections will require quite a bit more. The logical relationship between the various chapters can be roughly described by the diagram below. There are also five appendices, largely self-contained, which treat special topics. I. Arbitrary commutative rings I H. The ring of V. Miscellaneous IIl. Fields integers examples IV. Dedekind domains Contents Chapter r. Basie Coneepts . . . . . . . |
| Umfang: | 1 Online-Ressource (VIII, 150 p) |
| ISBN: | 9783642883309 9783642883323 |
| DOI: | 10.1007/978-3-642-88330-9 |
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| 490 | 1 | |a Ergebnisse der Mathematik und ihrer Grenzgebiete |v 73 | |
| 500 | |a The theory of quadratic forms and the intimately related theory of symmetric bilinear forms have a lang and rich his tory, highlighted by the work of Legendre, Gauss, Minkowski, and Hasse. (Compare [Dickson] and [Bourbaki, 24, p. 185].) Our exposition will concentrate on the relatively recent developments which begin with and are inspired by Witt's 1937 paper "Theorie der quadratischen Formen in beliebigen Körpern." We will be particularly interested in the work of A. Pfister and M. Knebusch. However, some older material will be described, particularly in Chapter II. The presentation is based on lectures by Milnor at the Institute for Advanced Study, and at Haverford College under the Phillips Lecture Program, during the Fall of 1970, as well as lectures at Princeton University in 1966. We want to thank J. Cunningham, M. Knebusch, M. Kneser, A. Rosenberg, W. Scharlau and J.-P. Serre for helpful suggestions and corrections. Prerequisites. The reader should be familiar with the rudiments of algebra, including for example the concept of tensor product for modules over a commutative ring. A few individual sections will require quite a bit more. The logical relationship between the various chapters can be roughly described by the diagram below. There are also five appendices, largely self-contained, which treat special topics. I. Arbitrary commutative rings I H. The ring of V. Miscellaneous IIl. Fields integers examples IV. Dedekind domains Contents Chapter r. Basie Coneepts . . . . . . . | ||
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Datensatz im Suchindex
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-88330-9 |
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| id | DE-604.BV042423090 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:10:48Z |
| institution | BVB |
| isbn | 9783642883309 9783642883323 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858507 |
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| physical | 1 Online-Ressource (VIII, 150 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1973 |
| publishDateSearch | 1973 |
| publishDateSort | 1973 |
| publisher | Springer Berlin Heidelberg |
| record_format | marc |
| series | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| spellingShingle | Milnor, John Symmetric Bilinear Forms Ergebnisse der Mathematik und ihrer Grenzgebiete Mathematics Mathematics, general Mathematik Quadratische Form (DE-588)4128297-8 gnd Bilinearform (DE-588)4138018-6 gnd |
| subject_GND | (DE-588)4128297-8 (DE-588)4138018-6 |
| title | Symmetric Bilinear Forms |
| title_auth | Symmetric Bilinear Forms |
| title_exact_search | Symmetric Bilinear Forms |
| title_full | Symmetric Bilinear Forms by John Milnor, Dale Husemoller |
| title_fullStr | Symmetric Bilinear Forms by John Milnor, Dale Husemoller |
| title_full_unstemmed | Symmetric Bilinear Forms by John Milnor, Dale Husemoller |
| title_short | Symmetric Bilinear Forms |
| title_sort | symmetric bilinear forms |
| topic | Mathematics Mathematics, general Mathematik Quadratische Form (DE-588)4128297-8 gnd Bilinearform (DE-588)4138018-6 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Quadratische Form Bilinearform |
| url | https://doi.org/10.1007/978-3-642-88330-9 |
| volume_link | (DE-604)BV005871160 |
| work_keys_str_mv | AT milnorjohn symmetricbilinearforms AT husemollerdale symmetricbilinearforms |