Geodesic
Indecomposable Positive Quadratic Forms
Canadian mathematical bulletin, Tome 33 (1990) no. 3, pp. 305-310

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Let F be a formally real field. A quadratic form q is called positive if sgnp ≧ 0 for all orderings P of F. A positive q is called decomposable if there exist positive forms q1, q2 such that q = q1⊥q2. Otherwise it is called indecomposable. In a first part we ask for which F there exist indecomposable three dimensional forms over F. We show that such forms exist iff F does not satisfy the property (A) defined in (J. K. Arason, A. Pfister: Zur Théorie der quadratischen Formen über formal reellen Körpern, Math Z. 153, 289-296 (1977)). We use an indecomposable three dimensional form defined by Arason and Pfister to construct indecomposable forms of arbitrary dimension. Then we examine the question for which fields F every positive form over F represents a nonzero sum of squares.
DOI : 10.4153/CMB-1990-049-1
Mots-clés : 11E04 
Krüskemper, Martin. Indecomposable Positive Quadratic Forms. Canadian mathematical bulletin, Tome 33 (1990) no. 3, pp. 305-310. doi: 10.4153/CMB-1990-049-1
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     title = {Indecomposable {Positive} {Quadratic} {Forms}},
     journal = {Canadian mathematical bulletin},
     pages = {305--310},
     year = {1990},
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     doi = {10.4153/CMB-1990-049-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1990-049-1/}
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