The Noether-Lefschetz theorem and sums of 4 squares in the rational function field
The Pythagoras number of some affine algebras and local algebras.
The reduced Wittring
The Undecidability of Pseudo Real Closed Fields.
Theoreme de Pfister pour les varietes et anneaux de Witt reduits.
Trace forms of central simple algebras.
Two theorems on regularly r-closed fields.
u-invariants of fields of characteristic 2.
Uniform denominators in Hilbert's Seventeenth Problem.
Von der Zerlegung der Discriminante der cubischen Gleichung, welche die Hauptaxen einer Fläche zweiter Ordnung bestimmen, in eine Summe von Quadraten.
Waring's problem for fields
If K is a field, denote by P(K,k) the a ∈ K which are sums of kth powers of elements of K, by P⁺(K,k) the set of a ∈ K which are sums of kth powers of totally positive elements of K. We give some simple conditions for which there exist integers w(K,k) and g(K,k) such that: a ∈ P(K,k) implies that a is the sum of at most w(K,k) kth powers; a ∈ P⁺(K,k) implies that a is the sum of at most g(K,k) totally positive kth powers. We apply the results to characterise functions that are sums of kth powers...
Zum Satz von Artin-Schreier über die Eindeutigkeit des reellen Abschlusses eines angeordneten Körpers.
Zur Theorie der quadratischen Formen über formalreellen Körpern.
Об отображении ограничения пространств порядков полей
Регулярно r-замкнутые поля