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Unramified extensions of quadratic fields

Progress in Natural Science: Materials International, 2008
Abstract Let K be a global quadratic field, then every unramified abelian extension of K is proved to be absolutely Galois when K is a number field or under some natural conditions when K is a function field. The absolute Galois group is also determined explicitly.
Li, Wei, Yang, Dong, Zhang, Xianke
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Quadratic Programming as an Extension of Classical Quadratic Maximization

Management Science, 1960
The article describes a procedure to maximize a strictly concave quadratic function subject to linear constraints in the form of inequalities. First the unconstrained maximum is considered; when certain constraints are violated, maximization takes place subject to each of these in equational (rather than inequality) form.
H. Theil, C. Van De Panne
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Quadratic Field Extensions

1999
To complete this lab, you should be familiar with the construction of quotient rings of the ring of polynomials over a field F. You should also be familiar with irreducible polynomials over a field. This lab does not presume any other prior knowledge of field extensions. Doing Ring Lab 10 first would be helpful, but it is not necessary.
Allen C. Hibbard, Kenneth M. Levasseur
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Embeddability of quadratic extensions in cyclic extensions

Forum Mathematicum, 2007
Summary: For an algebraic number field \(K\) we study the quadratic extensions of \(K\) which can be embedded in a cyclic extension of \(K\) of degree \(2^n\) for all natural numbers \(n\), as well as the quadratic extensions which can be embedded in an infinite normal extension with the additive group \(\mathbb Z_2=\lim_{\leftarrow}\mathbb Z/2^n ...
Geyer, W.-D., Jensen, Chr Ulrik
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Quadratic forms under algebraic extensions

Mathematische Annalen, 1976
Elman, Richard, Lam, T.Y.
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An Extension Theorem for Quadratic forms

Results in Mathematics, 1987
Mit Hilfe eines Fortsetzungssatzes, der sich auf quadratische Formen auf Unterräumen eines n-Vektorraumes mit \(4\leq n\leq \infty\) über kommutativem Körper bezieht, werden Aussagen über quadratische Mengen mindestens dreidimensionaler projektiver Räume bewiesen.
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Quadratic Forms. Friedrichs Extension.

2017
Let D be a linear subspace of a Hilbert space H.
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Hyperbolic Involutions and Quadratic Extensions

Communications in Algebra, 2010
This is a variation on a theme of Bayer-Fluckiger, Shapiro, and Tignol related to hyperbolic involutions. More precisely, criteria for the hyperbolicity of involutions of quadratic extensions of simple algebras and involutions of the form σ ⊗ τ and σ ⊗ ρ, where σ is an involution of a central simple algebra A, τ is the nontrivial automorphism of a ...
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Spheres of quadratic field extensions

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 1994
Sei \(L\) eine nichtkommutative quadratische Körpererweiterung des kommutativen Körpers \(K\). Der Autor stellt dann die projektive Gerade über \(L\) als Spread \(\varphi_{L/K}\) im dreidimensionalen projektiven Raum \(P\) über \(K\) dar. Als Menge von Geraden kann \(\varphi_{L/K}\) als Punktmenge auf der Kleinschen Quadrik im fünfdimensionalen ...
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Gauss bounds of quadratic extensions

Publicationes Mathematicae Debrecen, 1997
The author gives a very simple proof for the known theorem: ``Let \(K={{\mathbb Q}}(\sqrt{m})\) be a quadratic number field with ring of integers \({\mathbb Z}_K={\mathbb Z}[\omega]\) and discriminant \(\Delta,\) where \(\omega= \sqrt{m}\) if \(m\equiv 2\) or \(3 \pmod{4}\), \(\omega={(1+\sqrt{m}) / 2}\) if \(m\equiv 1 \pmod{4}\), \(\Delta=4m\) if \(m ...
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