Any F-torus of rank one is either split or isomorphic to the kernel of the norm of a quadratic extension.
2.
The elements of " Q " may be regarded as classifying graded quadratic extensions of " K ".
3.
In mathematics, trigonometry analogies are supported by the theory of quadratic extensions of finite fields, also known as Galois fields.
4.
These buildings arise when a quadratic extension of " L " acts on the vector space " L " 2.
5.
For " d " > 1 there are comparable cases for CM-fields, the complex quadratic extensions of totally real fields.
6.
;"'Kroneckerian field "': A totally real algebraic number field or a totally imaginary quadratic extension of a totally real field.
7.
This holds either already over the ground field, if " 1 is a square, or over the quadratic extension obtained by adjoining " i ".
8.
This is a significant extension of the theory of quadratic extensions, and the genus theory of quadratic forms ( linked to the 2-torsion of the class group ).
9.
That is, the ring of symmetric and alternating polynomials is a quadratic extension of the ring of symmetric polynomials, where one has adjoined a square root of the discriminant.
10.
So the Arf invariant of a nonsingular quadratic form over " K " is either zero or it describes a separable quadratic extension field of " K ".
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