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Grothendieck and Witt groups in the reduced theory of quadratic forms

Andrzej Sładek — 1980

Annales Polonici Mathematici

Abstract. Let F be a formally real field. Denote by G(F) and G t ( F ) the Grothen-dieck group of quadratic forms over F and its torsion subgroup, respectively. In this paper we study the structure of the factor group G ( F ) / G t ( F ) . This reduced Grothendieck group is a free Abelian group. The main results of the paper describe some sets of generators for G ( F ) / G t ( F ) , which in many cases allow us to find a basis for the group. Throughout the paper we use the language of the reduced theory of quadratic forms. In the final part...

Linear Dependence Of Powers Of Linear Forms

Andrzej Sładek — 2015

Annales Mathematicae Silesianae

The main goal of the paper is to examine the dimension of the vector space spanned by powers of linear forms. We also find a lower bound for the number of summands in the presentation of zero form as a sum of d-th powers of linear forms.

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