| dbo:abstract |
Die Pythagoraszahl eines Körpers ist definiert als das kleinste , so dass sich jede endliche Summe von Quadraten in schon als Summe von Quadraten schreiben lässt. (de) In mathematics, the Pythagoras number or reduced height of a field describes the structure of the set of squares in the field. The Pythagoras number p(K) of a field K is the smallest positive integer p such that every sum of squares in K is a sum of p squares. A Pythagorean field is a field with Pythagoras number 1: that is, every sum of squares is already a square. (en) En algèbre, le nombre de Pythagore d'un corps commutatif F est le plus petit entier naturel p tel que (dans F) toute somme finie de carrés soit somme de p carrés, si de tels entiers p existent, et l'infini sinon. On le note p(F). Le corps F est dit pythagoricien si p(F) = 1, c'est-à-dire si (dans F) toute somme de carrés est un carré. (fr) |
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Die Pythagoraszahl eines Körpers ist definiert als das kleinste , so dass sich jede endliche Summe von Quadraten in schon als Summe von Quadraten schreiben lässt. (de) In mathematics, the Pythagoras number or reduced height of a field describes the structure of the set of squares in the field. The Pythagoras number p(K) of a field K is the smallest positive integer p such that every sum of squares in K is a sum of p squares. A Pythagorean field is a field with Pythagoras number 1: that is, every sum of squares is already a square. (en) En algèbre, le nombre de Pythagore d'un corps commutatif F est le plus petit entier naturel p tel que (dans F) toute somme finie de carrés soit somme de p carrés, si de tels entiers p existent, et l'infini sinon. On le note p(F). Le corps F est dit pythagoricien si p(F) = 1, c'est-à-dire si (dans F) toute somme de carrés est un carré. (fr) |
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Pythagoraszahl (de) Nombre de Pythagore (fr) Pythagoras number (en) |
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