Universal quadratic forms over multiquadratic fields
نویسندگان
چکیده
منابع مشابه
Quadratic Forms over Arbitrary Fields
Introduction. Witt [5] proved that two binary or ternary quadratic forms, over an arbitrary field (of characteristic not 2) are equivalent if and only if they have the same determinant and Hasse invariant. His proof is brief and elegant but uses a lot of the theory of simple algebras. The purpose of this note is to make this fundamental theorem more accessible by giving a short proof using only...
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Let Fq be a finite field with q elements and let X be a set of matrices over Fq. The main results of this paper are explicit expressions for the number of pairs (A,B) of matrices in X such that A has rank r, B has rank s, and A + B has rank k in the cases that (i) X is the set of alternating matrices over Fq and (ii) X is the set of symmetric matrices over Fq for odd q. Our motivation to study ...
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1. Four equivalent definitions of a quadratic form 2 2. Action of Mn(K) on n-ary quadratic forms 4 3. The category of quadratic spaces 7 4. Orthogonality in quadratic spaces 9 5. Diagonalizability of Quadratic Forms 11 6. Isotropic and hyperbolic spaces 13 7. Witt’s theorems: statements and consequences 15 8. Orthogonal groups, reflections and the proof of Witt Cancellation 17 8.1. The orthogon...
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ژورنال
عنوان ژورنال: The Ramanujan Journal
سال: 2017
ISSN: 1382-4090,1572-9303
DOI: 10.1007/s11139-017-9965-7