Document Zbl 0277.15013

Elman, Richard; Lam, Tsit-Yuen; Prestel, Alexander

On some Hasse principles over formally real fields. (English) Zbl 0277.15013

Math. Z. 134, 291-301 (1973).

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MSC:

11E81	Algebraic theory of quadratic forms; Witt groups and rings
12D15	Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
12J15	Ordered fields

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References:

[1]	Arason, J.K., Pfister, A.: Beweis des Krullschen Durchschnittsatzes für den Wittring. Inventiones. Math.12, 173-176 (1971) · Zbl 0212.37302
[2]	Artin, E.: Elements of Algebraic Geometry. New York: New York University, 1955 · Zbl 0065.25703
[3]	Bröcker, L.: Über eine Klasse pythagoriescher Körper. Arch. der Math.23, 405-407 (1972) · Zbl 0251.12102 · doi:10.1007/BF01304904
[4]	Elman, R., Lam, T.Y.: Pfister forms andK-theory of fields. J. Algebra23, 181-213 (1972) · Zbl 0246.15029 · doi:10.1016/0021-8693(72)90054-3
[5]	Elman, R., Lam, T.Y.: Quadratic forms over formally real fields and pythagorean fields. Amer. J. Math.94, 1155-1194 (1972) · Zbl 0259.12101 · doi:10.2307/2373568
[6]	Elman, R., Lam, T.Y.: Quadratic forms and theu-invariant, I. Math. Z.131, 283-304 (1973) · doi:10.1007/BF01174904
[7]	Elman, R., Lam, T.Y.: Quadratic forms and theu-invariant, II. To appear in Inventiones Math.21, 125-137 (1973) · Zbl 0267.10029 · doi:10.1007/BF01389692
[8]	Elman, R., Lam, T.Y.: On the quaternion symbol homonorphismg F :k 2 F?B(F). In: Proc. of the Seattle Conference on AlgebraicK-theory (1973). Springer Lecture Notes342, 447-463. Berlin-Heidelberg-New York: Springer 1973 · Zbl 0267.10030
[9]	Gupta, H.N., Prestel, A.: Triangle and Schwarz inequality in Pasch-free euclidean geometry. Bull. Acad. Polon. Sci., Sér. Sci. math., astron., phys.20, 999-1003 (1972) · Zbl 0312.06015
[10]	Knebusch, M., Rosenberg, A., Ware, R.: Structure of Witt rings, quotients of abelian group rings, and orderings of fields. Bull. Amer. math. Soc.77, 205-210 (1971) · Zbl 0213.05001 · doi:10.1090/S0002-9904-1971-12683-6
[11]	Lam, T.Y.: The Algebraic Theory of Quadratic Forms. Benjamin, 1973 · Zbl 0259.10019
[12]	Pfister, A.: Quadratische Formen in beliebigen Körpern. Inventiones Math.1, 116-132 (1966) · Zbl 0142.27203 · doi:10.1007/BF01389724
[13]	Prestel, A.: Quadratische Semi-Ordnungen und quadratische Formen. To appear in Math. Z.133, 319-342 (1973) · Zbl 0275.12013 · doi:10.1007/BF01177872
[14]	Prestel, A.: Euklidische Geometrie ohne das Axiom von Pasch. To appear in Abh. math. Sem. Univ. Hamburg 41 · Zbl 0288.50003
[15]	Prestel, A., Ziegler, M.: Erblich euklidische Körper. To appear in J. reine angew. Math.
[16]	Scharlau, W.: Quadratic reciprocity laws. J. Number Theory4, 78-97 (1972) · Zbl 0241.12005 · doi:10.1016/0022-314X(72)90012-1
[17]	Witt, E.: Theorie der quadratischen Formen in beliebigen Körpern. J. reine angew. Math.176, 31-44 (1937) · Zbl 0015.05701 · doi:10.1515/crll.1937.176.31

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