Document Zbl 0421.10015

Über die Stufe von Dedekind Ringen. (German) Zbl 0421.10015

Arch. Math. 33, 226-231 (1979).

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MSC:

11E16	General binary quadratic forms
12D15	Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
13F05	Dedekind, Prüfer, Krull and Mori rings and their generalizations
13H99	Local rings and semilocal rings

Keywords:

level of a ring; Dedekind rings; quadratic forms; sum of squares; pythagoras number

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References:

[1]	R.Baeza, Quadratic forms over semilocal rings. LNM655, Berlin-Heidelberg-New York 1978. · Zbl 0382.10014
[2]	J. L.Colliot-Th?lene, Formes quadratiques sur les anneaux semilocaux reguliers. Erscheint demn?chst in Bull. Math. Soc. de France.
[3]	T. Craven, A. Rosenberg, andR. Ware, The map of the Witt ring of a domain into the Witt ring of its field of fractions. Proc. Am. Math. Soc.51, 25-30 (1975). · Zbl 0313.13025 · doi:10.1090/S0002-9939-1975-0384789-1
[4]	P.Draxl, La repr?sentation de ? 1 comme somme de carr?s dans les ordres d’un corps de nombres algebriques. Journ?es arithmetiques fran?aises, Marseille 1971.
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[7]	M.Knebusch, Grothendieck- und Wittringe von nicht ausgearteten symmetrischen Bilinearformen. Sitz. ber. Heidelberger Akad. Wiss. Math. naturwiss. Kl. 1969/70, 3. Abh., 93-157.
[8]	M.Knebusch, Symmetric bilinear forms over algebraic varietes. Conference on quadratic forms 1976. Ed. G. Orzech. Queen’s papers in pure and appl. Math.46 (1977).
[9]	M. Knebusch, Generalisation of a theorem of Artin-Pfister to arbitrary semi-local rings and related topics. J. Algebra,36, 46-67 (1975). · Zbl 0315.13014 · doi:10.1016/0021-8693(75)90154-4
[10]	M. Kneser, Klassenzahlen indefiniter quadratischer Formen in drei oder mehr Ver?nderlichen. Arch. Math.7, 323-332 (1956). · Zbl 0071.27205 · doi:10.1007/BF01900681
[11]	O. T.O’Meara, Introduction to quadratic Forms. Berlin-Heidelberg-New York 1963.
[12]	M. Peters, Die Stufe von Ordnungen ganzer Zahlen in algebraischen Zahlk?rpern. Math. Ann.195, 309-314 (1972). · doi:10.1007/BF01423616
[13]	M. Peters, Summen von Quadraten in Zahlringen. J. Reine Angew. Math.268/269, 318-323 (1974). · Zbl 0287.10034 · doi:10.1515/crll.1974.268-269.318

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