## Introduction to Quadratic Forms over Fields |

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### Contents

xi | |

1 | |

Introduction to Witt Rings | 27 |

Quaternion Algebras and their Norm Forms | 51 |

The BrauerWall Group | 79 |

Clifford Algebras | 103 |

Local Fields and Global Fields | 143 |

Quadratic Forms Under Algebraic Extensions | 187 |

Formally Real Fields RealClosed Fields and Pythagorean Fields | 231 |

Quadratic Forms under Transcendental Extensions | 299 |

Pfister Forms and Function Fields | 315 |

Field Invariants | 375 |

Special Topics in Quadratic Forms | 425 |

Special Topics on Invariants | 479 |

### Common terms and phrases

anisotropic anisotropic form anisotropic over F assume binary form Chapter clearly closed field construction Corollary CSGA defined denote dim q division algebra element equation equivalent euclidean exists extension K/F extension of F F is formally F is nonreal F-algebra F-form fact field extension field F finite field form over F form q formally real field function field graded algebra hence homomorphism hyperbolic implies induction integer isometry isomorphism Lemma Let F Let q multiplicative n-fold Pfister form nonreal fields nonzero notation number field orthogonal Pfister form Pfister neighbor polynomial prime ideal Proof Proposition prove Pythagoras number pythagorean field q is isotropic quadratic extension quadratic form quadratic form theory quadratic space quadratically closed quaternion algebras real-closed field result splits square classes squares in F subform subgroup Theorem torsion u-invariant unique vector Witt ring write Wt(F zero

### Popular passages

Page xviii - the ones that I know Are simply not so When the characteristic is two!

### References to this book

The Classical Fields: Structural Features of the Real and Rational Numbers H. Salzmann Limited preview - 2007 |