Quadratic forms permitting triple composition

Composition of Binary Quadratic Forms

Norm Principles for Forms of Higher Degree Permitting Composition

Let F be a field of characteristic 0 or greater than d. Scharlau’s norm principle holds for separable field extensions K over F , for certain forms φ of degree d over F which permit composition. Introduction Let d ≥ 2 be an integer and let F be a field of characteristic 0 or > d. Let φ : V → F be a form of degree d on an F -vector space V of dimension n (i.e., after suitable identification, φ i...

Applications of quadratic D-forms to generalized quadratic forms

In this paper, we study generalized quadratic forms over a division algebra with involution of the first kind in characteristic two. For this, we associate to every generalized quadratic from a quadratic form on its underlying vector space. It is shown that this form determines the isotropy behavior and the isometry class of generalized quadratic forms.

A Generalized Composition of Quadratic Forms based on Quadratic Pairs

For quadratic spaces which represent 1 there is a characterization of hermitian compositions in the language of algebras-with-involutions using the even Clifford algebra. We extend this notion to define a generalized composition based on quadratic pairs and determine the degrees of minimal compositions for any given quadratic pair.

On the Composition of Quadratic Forms.

The fundamental problem of this theory is to determine a compound of two given forms and the transformation under which the relationship exists. This problem has been considered f by Gauss, Arndt, Dedekind and others. The method of DedekindJ was based upon a correspondence between forms and moduls in an algebraic field, composition of forms corresponding to multiplication of moduls. The method ...