Bilinear Algebra : an Introduction to the Algebraic Theory of Quadratic Forms /

"Giving an easily accessible elementary introduction to the algebraic theory of quadratic forms, this book covers both Witt's theory and Pfister's theory of quadratic forms. Leading topics include the geometry of bilinear spaces, classification of bilinear spaces up to isometry depend...

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Bibliographic Details
Main Author: Szymiczek, Kazimierz (Author)
Corporate Author: Taylor & Francis
Format: eBook
Language:English
Published: London : Taylor and Francis, 2017.
Edition:First edition.
Subjects:
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Part, I Bilinear spaces / Kazimierz Szymiczek
  • chapter 1 Introduction / Kazimierz Szymiczek
  • chapter 2 Bilinear spaces / Kazimierz Szymiczek
  • chapter 3 Bases and matrices of bilinear spaces / Kazimierz Szymiczek
  • chapter 4 Isometries of bilinear spaces / Kazimierz Szymiczek
  • chapter 5 Nonsingular bilinear spaces / Kazimierz Szymiczek
  • chapter 6 Diagonalization of bilinear spaces / Kazimierz Szymiczek
  • chapter 7 Witt's cancellation theorem / Kazimierz Szymiczek
  • chapter 8 Witt's chain isometry theorem / Kazimierz Szymiczek
  • chapter 9 Symmetric spaces over some fields / Kazimierz Szymiczek
  • chapter 10 Isometry groups / Kazimierz Szymiczek
  • part, II Witt rings / Kazimierz Szymiczek
  • chapter 11 Metabolic and hyperbolic spaces / Kazimierz Szymiczek
  • chapter 12 Witt decomposition of symmetric spaces / Kazimierz Szymiczek
  • chapter 13 Witt group / Kazimierz Szymiczek
  • chapter 14 Tensor products / Kazimierz Szymiczek
  • chapter 15 Witt ring / Kazimierz Szymiczek
  • chapter 16 Quadratic forms / Kazimierz Szymiczek
  • chapter 17 Pfister forms / Kazimierz Szymiczek
  • chapter 18 Formally real fields and ordered fields / Kazimierz Szymiczek
  • chapter 19 Prime ideals of the Witt ring / Kazimierz Szymiczek
  • chapter 20 Witt equivalence of fields / Kazimierz Szymiczek
  • part, III Invariants / Kazimierz Szymiczek
  • chapter 21 Algebras / Kazimierz Szymiczek
  • chapter 22 Quaternion algebras / Kazimierz Szymiczek
  • chapter 23 Tensor product of algebras / Kazimierz Szymiczek
  • chapter 24 Brauer group / Kazimierz Szymiczek
  • chapter 25 Hasse and Witt invariants / Kazimierz Szymiczek.