symmetric bilinear forms (50 Ergebnisse)

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Hardcover. Zustand: new. Hardcover. A Mathematician Said Who Can Quote Me a Theorem thats True? For the ones that I Know Are Simply not So, When the Characteristic is Two! This pretty limerick ?rst came to my ears in May 1998 during a talk by T.Y. Lam 1 on ?eld invariants from the theory of quadratic forms. It ispoetic exaggeration alloweda suitable motto for this monograph. What is it about? At the beginning of the seventies I drew up a specialization theoryofquadraticandsymmetricbilinear formsover ?elds[32].Let? : K? L?? be a place. Then one can assign a form? (?)toaform? over K in a meaningful way ? if? has good reduction with respect to? (see1.1). The basic idea is to simply apply the place? to the coe?cients of?, which must therefore be in the valuation ring of? The specialization theory of that time was satisfactory as long as the ?eld L, and therefore also K, had characteristic 2. It served me in the ?rst place as the foundation for a theory of generic splitting of quadratic forms [33], [34]. After a very modest beginning, this theory is now in full bloom. It became important for the understanding of quadratic forms over ?elds, as can be seen from the book [26]of IzhboldinKahnKarpenkoVishik for instance. One should note that there exists a theoryof(partial)genericsplittingofcentralsimplealgebrasandreductivealgebraic groups, parallel to the theory of generic splitting of quadratic forms (see [29] and the literature cited there). It served me in the ?rst place as the foundation for a theory of generic splitting of quadratic forms [33], [34]. One should note that there exists a theoryof(partial)genericsplittingofcentralsimplealgebrasandreductivealgebraic groups, parallel to the theory of generic splitting of quadratic forms (see [29] and the literature cited there). Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

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Paperback. Zustand: new. Paperback. The theory cf quadratic forms and the intimately related theory of sym- metrie 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 rela- tively recent developments which begin with and are inspired by Witt's 1937 paper "Theorie der quadratischen Formen in beliebigen Korpern." 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 Ad- vanced Study, and at Haverford College under the Phillips Lecture Pro- gram, during the Fall of 1970, as weIl as Iectures at Princeton University il1 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., incJuding for example the concept of tensor product for mo- dules 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 . The theory cf quadratic forms and the intimately related theory of symA metrie 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 relaA tively recent developments which begin with and are inspired by Witt's 1937 paper "Theorie der quadratischen Formen in beliebigen KArpern." 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 AdA vanced Study, and at Haverford College under the Phillips Lecture ProA gram, during the Fall of 1970, as weIl as Iectures at Princeton University il1 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., incJuding for example the concept of tensor product for moA dules 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 . . . . . Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - A Mathematician Said Who Can Quote Me a Theorem that's True For the ones that I Know Are Simply not So, When the Characteristic is Two! This pretty limerick rst came to my ears in May 1998 during a talk by T.Y. Lam 1 on eld invariants from the theory of quadratic forms. It is-poetic exaggeration allowed-a suitable motto for this monograph. What is it about At the beginning of the seventies I drew up a specialization theoryofquadraticandsymmetricbilinear formsover elds[32].Let : K L be a place. Then one can assign a form ( )toaform over K in a meaningful way if has 'good reduction' with respect to (see1.1). The basic idea is to simply apply the place to the coe cients of , which must therefore be in the valuation ring of . The specialization theory of that time was satisfactory as long as the eld L, and therefore also K, had characteristic 2. It served me in the rst place as the foundation for a theory of generic splitting of quadratic forms [33], [34]. After a very modest beginning, this theory is now in full bloom. It became important for the understanding of quadratic forms over elds, as can be seen from the book [26]of Izhboldin-Kahn-Karpenko-Vishik for instance. One should note that there exists a theoryof(partial)genericsplittingofcentralsimplealgebrasandreductivealgebraic groups, parallel to the theory of generic splitting of quadratic forms (see [29] and the literature cited there).

Buch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - A Mathematician Said Who Can Quote Me a Theorem that's True For the ones that I Know Are Simply not So, When the Characteristic is Two! This pretty limerick rst came to my ears in May 1998 during a talk by T.Y. Lam 1 on eld invariants from the theory of quadratic forms. It is-poetic exaggeration allowed-a suitable motto for this monograph. What is it about At the beginning of the seventies I drew up a specialization theoryofquadraticandsymmetricbilinear formsover elds[32].Let : K L be a place. Then one can assign a form ( )toaform over K in a meaningful way if has 'good reduction' with respect to (see1.1). The basic idea is to simply apply the place to the coe cients of , which must therefore be in the valuation ring of . The specialization theory of that time was satisfactory as long as the eld L, and therefore also K, had characteristic 2. It served me in the rst place as the foundation for a theory of generic splitting of quadratic forms [33], [34]. After a very modest beginning, this theory is now in full bloom. It became important for the understanding of quadratic forms over elds, as can be seen from the book [26]of Izhboldin-Kahn-Karpenko-Vishik for instance. One should note that there exists a theoryof(partial)genericsplittingofcentralsimplealgebrasandreductivealgebraic groups, parallel to the theory of generic splitting of quadratic forms (see [29] and the literature cited there).

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Hardcover. Zustand: new. Hardcover. A Mathematician Said Who Can Quote Me a Theorem thats True? For the ones that I Know Are Simply not So, When the Characteristic is Two! This pretty limerick ?rst came to my ears in May 1998 during a talk by T.Y. Lam 1 on ?eld invariants from the theory of quadratic forms. It ispoetic exaggeration alloweda suitable motto for this monograph. What is it about? At the beginning of the seventies I drew up a specialization theoryofquadraticandsymmetricbilinear formsover ?elds[32].Let? : K? L?? be a place. Then one can assign a form? (?)toaform? over K in a meaningful way ? if? has good reduction with respect to? (see1.1). The basic idea is to simply apply the place? to the coe?cients of?, which must therefore be in the valuation ring of? The specialization theory of that time was satisfactory as long as the ?eld L, and therefore also K, had characteristic 2. It served me in the ?rst place as the foundation for a theory of generic splitting of quadratic forms [33], [34]. After a very modest beginning, this theory is now in full bloom. It became important for the understanding of quadratic forms over ?elds, as can be seen from the book [26]of IzhboldinKahnKarpenkoVishik for instance. One should note that there exists a theoryof(partial)genericsplittingofcentralsimplealgebrasandreductivealgebraic groups, parallel to the theory of generic splitting of quadratic forms (see [29] and the literature cited there). It served me in the ?rst place as the foundation for a theory of generic splitting of quadratic forms [33], [34]. One should note that there exists a theoryof(partial)genericsplittingofcentralsimplealgebrasandreductivealgebraic groups, parallel to the theory of generic splitting of quadratic forms (see [29] and the literature cited there). Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability.

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