Symmetric Bilinear Forms:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1973
|
| Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete
73 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | 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 . . . . . . . |
| Physical Description: | 1 Online-Ressource (VIII, 150 p) |
| ISBN: | 9783642883309 9783642883323 |
| DOI: | 10.1007/978-3-642-88330-9 |
Staff View
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| isbn | 9783642883309 9783642883323 |
| language | English |
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| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| spelling | Milnor, John Verfasser aut Symmetric Bilinear Forms by John Milnor, Dale Husemoller Berlin, Heidelberg Springer Berlin Heidelberg 1973 1 Online-Ressource (VIII, 150 p) txt rdacontent c rdamedia cr rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete 73 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 . . . . . . . Mathematics Mathematics, general Mathematik Quadratische Form (DE-588)4128297-8 gnd rswk-swf Bilinearform (DE-588)4138018-6 gnd rswk-swf Bilinearform (DE-588)4138018-6 s 1\p DE-604 Quadratische Form (DE-588)4128297-8 s 2\p DE-604 Husemoller, Dale Sonstige oth Ergebnisse der Mathematik und ihrer Grenzgebiete 73 (DE-604)BV005871160 73 https://doi.org/10.1007/978-3-642-88330-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| 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 |